Jan Sokolowski

Approximation of Boundary Control Problems on Curved Domains. II - The Dirichlet Case (2009)

In this paper we consider a Neumann control problem associated to a semilinear elliptic equation defined in a curved domain $\Omega$. To deal with the numerical analysis of this problem, the...

Approximation of Boundary Control Problems on Curved Domains. I - The Neumann Case (2009)

The influence of small boundary variations of the domain on optimal controls is investigated in this paper. The domain variations are governed by a small parameter $h\to 0$. In a previous paper we...

Approximation of Boundary Control Problems on Curved Domains. II - The Dirichlet Case (2009)

In this paper we consider a Neumann control problem associated to a semilinear elliptic equation defined in a curved domain $\Omega$. To deal with the numerical analysis of this problem, the...

Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity (2009)

The influence of small boundary variations of the domain on optimal controls is investigated in this paper. The domain variations are governed by a small parameter $h\to 0$. In a previous paper we...

Consiglieri, Luisa, Necasova, Sarka, Sokolowski, Jan

We prove the existence and uniqueness of weak solutions to the variational formulation of the Maxwell-Boussinesq approximation problem. Some further regularity in $W^{1,2+\delta}$, $\delta>0$, is...

Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity (2009)

Consiglieri, Luisa, Necasova, Sarka, Sokolowski, Jan

We prove the existence and uniqueness of weak solutions to the variational formulation of the Maxwell-Boussinesq approximation problem. Some further regularity in $W^{1,2+\delta}$, $\delta>0$, is...

Shape Sensitivity Analysis of a Quasi-Eletrostatic Piezoelectric System in Multilayered Media (2009)

Leugering, Guenter, Novotny, Andre, Perla Menzala, Augusto, Sokolowski, Jan

The optimization of shape and topology of piezo-patches or layered piezo-electrical material attached to structural parts, like elastic bodies, plates and shells plays a major role in the design of...

Shape Sensitivity Analysis of a Quasi-Eletrostatic Piezoelectric System in Multilayered Media (2009)

Leugering, Guenter, Novotny, Andre, Perla Menzala, Augusto, Sokolowski, Jan

The optimization of shape and topology of piezo-patches or layered piezo-electrical material attached to structural parts, like elastic bodies, plates and shells plays a major role in the design of...

Neumann Laplacian on a domain with tangential components in the boundary (2008)

Nazarov, Sergeï A., Sokolowski, Jan, Taskinen, Jari

We study the Neumann problem for the Poisson equation in a domain where two boundary components are tangential at a single point, such that a geometrical irregularity of the rotational cusp type is...

Asymptotic of solutions of the Neumann problem in a domain with closely posed components of the boundary (2008)

Cardone, Giuseppe, Nazarov, Sergeï A., Sokolowski, Jan

The Neumann problem for the Poisson equation is considered in a domain $\Omega_{\varepsilon}\subset\mathbb{R}^{n}$ with boundary components posed at a small distance $\varepsilon>0$ so that in the...

SPECTRAL PROBLEMS IN ELASTICITY. SINGULAR BOUNDARY PERTURBATIONS (2008)

SPECTRAL PROBLEMS IN ELASTICITY. SINGULAR BOUNDARY PERTURBATIONS (2008)

The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies...

Neumann Laplacian on a domain with tangential components in the boundary (2008)

The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies...

Nazarov, Sergeï A., Sokolowski, Jan, Taskinen, Jari

We study the Neumann problem for the Poisson equation in a domain where two boundary components are tangential at a single point, such that a geometrical irregularity of the rotational cusp type is...

Asymptotic of solutions of the Neumann problem in a domain with closely posed components of the boundary (2008)

Cardone, Giuseppe, Nazarov, Sergeï A., Sokolowski, Jan

The Neumann problem for the Poisson equation is considered in a domain $\Omega_{\varepsilon}\subset\mathbb{R}^{n}$ with boundary components posed at a small distance $\varepsilon>0$ so that in the...

Topological sensitivity analysis for elliptic problems on graphs (2008)

Topological sensitivity analysis for elliptic problems on graphs (2008)

We consider elliptic problems on graphs under given loads and bilateral contact conditions. We ask the question which graph is best suited to sustain the loads and the constraints. More precisely,...

Topological derivatives for semilinear elliptic equations (2008)

We consider elliptic problems on graphs under given loads and bilateral contact conditions. We ask the question which graph is best suited to sustain the loads and the constraints. More precisely,...

Iguernane, Mohamed, Nazarov, Sergueï A., Roche, Jean-Rodolphe, Sokolowski, Jan, Szulc, Katarzyna

The form of topological derivatives for integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological...

Topological derivatives in piezoelectricity (2008)

Cardone, Giuseppe, Nazarov, Sergeï, Sokolowski, Jan

Asymptotic formulae for the mechanical and electric fields in a piezoelectric body with a small void are derived and justified. Such results are new and useful for applications in the field of design...

Shape and topological sensitivity analysis in domains with cracks (2008)

Khludnev, Alexander, Sokolowski, Jan, Szulc, Katarzyna

Framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. Equilibrium problem for elastic body with cracks...

Topological derivatives for semilinear elliptic equations (2008)

Iguernane, Mohamed, Nazarov, Sergueï A., Roche, Jean-Rodolphe, Sokolowski, Jan, Szulc, Katarzyna

The form of topological derivatives for integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological...

Topological derivatives in piezoelectricity (2008)

Cardone, Giuseppe, Nazarov, Sergeï, Sokolowski, Jan

Asymptotic formulae for the mechanical and electric fields in a piezoelectric body with a small void are derived and justified. Such results are new and useful for applications in the field of design...

Shape and topological sensitivity analysis in domains with cracks (2008)

Khludnev, Alexander, Sokolowski, Jan, Szulc, Katarzyna

Framework for shape and topology sensitivity analysis in geometrical domains with cracks is established for elastic bodies in two spatial dimensions. Equilibrium problem for elastic body with cracks...

SHAPE SENSITIVITY ANALYSIS OF EIGENVALUES REVISITED (2008)

SHAPE SENSITIVITY ANALYSIS OF EIGENVALUES REVISITED (2008)

The paper can be considered as a complement to previous papers of the authors. An insight into applied asymptotic analysis of boundary value problems in singularly perturbed domains is presented. As...

Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions (2008)

The paper can be considered as a complement to previous papers of the authors. An insight into applied asymptotic analysis of boundary value problems in singularly perturbed domains is presented. As...

Khludnev, Alexander, Novotny, Andre, Sokolowski, Jan, Zochowski, Antoni

We consider a 3D elastic body with a rigid inclusion and a crack located at the boundary of the inclusion. It is assumed that non-penetration conditions are imposed at the crack faces which do not...

Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions (2008)

Khludnev, Alexander, Novotny, Andre, Sokolowski, Jan, Zochowski, Antoni

We consider a 3D elastic body with a rigid inclusion and a crack located at the boundary of the inclusion. It is assumed that non-penetration conditions are imposed at the crack faces which do not...

On Solvability Of Boundary Value Problems In Elastoplasticity (2007)

Alexander M. Khludnev, Jan Sokolowski, Er M. Khludnev, Projet Numath

: In the paper the existence of a solution to the three dimensional elastoplastic problem with the Prandtl-Reuss constitutive law and the Neumann boundary conditions is obtained. The proof is based...

Calculating Tangent Sets to Certain Sets in Functional Spaces (2007)

Ewa Bednarczuk, Ewa Bednarczuk, Michel Pierre, Jan Sokolowski, Michel Pierre, Elisabeth Rouy, ...

: We give necessary and sufficient conditions for a given element to be a member of the second order tangent set T 00 K (f; v) to the positive cone K in L 1 : Since, in general T 00 K (f; v) may be...

Asymptotic analysis and topological derivatives for shape and topology optimization of elasticity problems in two spactial dimensions (2007)

Energy change in elastic solids due to a spherical or circular cavity, considering uncertain in put data (2007)

Topological derivatives for elasticity problems are used in shape and topology optimization in structural mechanics. We propose an approach to the asymptotic analysis of singular perturbations of...

Hlavacek, I., Novotny, A.A., Sokolowski, Jan, Zochowski, Antoni

In the paper we consider topological derivative of shape functionals for elasticity, which is used to derive the worst and also the maximum range scenarios for behavior of elastic body in case of...

Spectral problems in the shape optimisation, singular boundary perturbations (2007)

Inhomogeneous boundary value problems for compressible Navier-Stokes and transport equations (2007)

In the paper asymptotic analysis of spectral problems is performed for singular pertrurbations of geometrical domains. Asymptotic approximations of eigenvalues and eigenfunctions are constructed for...

Plotnikov, Pavel I., Ruban, Evgenya V., Sokolowski, Jan

In the paper compressible, stationary Navier-Stokes eqautions are considered. A framework for analysis of such equations is established. The well-posedness for homogeneous boundary value problems of...

Inhomogeneous boundary value problems for compressible Navier-Stokes and transport equations (2007)

Plotnikov, Pavel I., Ruban, Evgenya V., Sokolowski, Jan

In the paper compressible, stationary Navier-Stokes eqautions are considered. A framework for analysis of such equations is established. The well-posedness for homogeneous boundary value problems of...

Spectral problems in the shape optimisation, singular boundary perturbations (2007)

Energy change in elastic solids due to a spherical or circular cavity, considering uncertain in put data (2007)

In the paper asymptotic analysis of spectral problems is performed for singular pertrurbations of geometrical domains. Asymptotic approximations of eigenvalues and eigenfunctions are constructed for...

Hlavacek, I., Novotny, A.A., Sokolowski, Jan, Zochowski, Antoni

In the paper we consider topological derivative of shape functionals for elasticity, which is used to derive the worst and also the maximum range scenarios for behavior of elastic body in case of...

Asymptotic analysis and topological derivatives for shape and topology optimization of elasticity problems in two spactial dimensions (2007)

Topological derivatives for elliptic problems on graphs (2006)

Topological derivatives for elasticity problems are used in shape and topology optimization in structural mechanics. We propose an approach to the asymptotic analysis of singular perturbations of...

Topological derivatives for elliptic problems on graphs (2006)

We consider elliptic problems on graphs under given loads. We ask the question which graph is best suited to sustain the loads. More precisely, given a cost function we may look at a multiple node of...

A levelset method in shape and topology optimization for variational inequalities (2006)

We consider elliptic problems on graphs under given loads. We ask the question which graph is best suited to sustain the loads. More precisely, given a cost function we may look at a multiple node of...

Fulmanski, Piotr, Laurain, Antoine, Scheid, Jean-Francois, Sokolowski, Jan

Levelset method is used for shape optimization of the energy functional for Signorini problem. The topological derivatives are employed for the topology variations in the form of small holes....

A levelset method in shape and topology optimization for variational inequalities (2006)

Fulmanski, Piotr, Laurain, Antoine, Scheid, Jean-Francois, Sokolowski, Jan

Levelset method is used for shape optimization of the energy functional for Signorini problem. The topological derivatives are employed for the topology variations in the form of small holes....

Modeling of topological derivatives for contact problems (2006)

Concentrations of solutions to time-discretizied compressible Navier-Stokes equations (2006)

The form of topological derivatives for shape functionals for contact problems is established. Methods of numerical evaluation of such derivatives are proposed and compared.

Plotnikov, Pavel Igorevich, Sokolowski, Jan

The compactness properties of solutions to time-discretization of compressible Navier-Stokes equations are investigated in three dimensions. The existence of generalized solutions is established.

Modeling of topological derivatives for contact problems (2006)

Concentrations of solutions to time-discretizied compressible Navier-Stokes equations (2006)

The form of topological derivatives for shape functionals for contact problems is established. Methods of numerical evaluation of such derivatives are proposed and compared.

Plotnikov, Pavel Igorevich, Sokolowski, Jan

The compactness properties of solutions to time-discretization of compressible Navier-Stokes equations are investigated in three dimensions. The existence of generalized solutions is established.

Topological derivatives for elliptic problems on graphs (2006)

A levelset method in shape and topology optimization for variational inequalities (2006)

We consider elliptic problems on graphs under given loads. We ask the question which graph is best suited to sustain the loads. More precisely, given a cost function we may look at a multiple node of...

Fulmanski, Piotr, Laurain, Antoine, Scheid, Jean-Francois, Sokolowski, Jan

Levelset method is used for shape optimization of the energy functional for Signorini problem. The topological derivatives are employed for the topology variations in the form of small holes....

Analysis of crack singularities in an aging elastic material (2006)

Costabel, Martin, Dauge, Monique, A. Nazarov, Sergei, Sokolowski, Jan

We consider a quasistatic system involving a Volterra kernel modelling an hereditarily-elastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of...

Inhomogeneous boundary value problems for compressible Navier-Stokes equation: well-posedness and sensitivity analysis (2006)

Plotnikov, Pavel I., Ruban, Evgenya V., Sokolowski, Jan

In the paper compressible, stationary Navier-Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary...

Analysis of crack singularities in an aging elastic material (2006)

Costabel, Martin, Dauge, Monique, A. Nazarov, Sergei, Sokolowski, Jan

We consider a quasistatic system involving a Volterra kernel modelling an hereditarily-elastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of...

Inhomogeneous boundary value problems for compressible Navier-Stokes equation: well-posedness and sensitivity analysis (2006)

Plotnikov, Pavel I., Ruban, Evgenya V., Sokolowski, Jan

In the paper compressible, stationary Navier-Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary...

Topological derivatives for elliptic problems on graphs (2006)

A levelset method in shape and topology optimization for variational inequalities (2006)

We consider elliptic problems on graphs under given loads. We ask the question which graph is best suited to sustain the loads. More precisely, given a cost function we may look at a multiple node of...

Fulmanski, Piotr, Laurain, Antoine, Scheid, Jean-Francois, Sokolowski, Jan

Levelset method is used for shape optimization of the energy functional for Signorini problem. The topological derivatives are employed for the topology variations in the form of small holes....

Analysis of crack singularities in an aging elastic material (2006)

Costabel, Martin, Dauge, Monique, Nazarov, Sergeï A., Sokolowski, Jan

Analysis of crack singularities in an aging elastic material (2005)

Costabel, Martin, Dauge, Monique, A. Nazarov, Sergei, Sokolowski, Jan

We consider a quasistatic system involving a Volterra kernel modelling an hereditarily-elastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of...

Analysis of crack singularities in an aging elastic material (2005)

Costabel, Martin, Dauge, Monique, A. Nazarov, Sergei, Sokolowski, Jan

We consider a quasistatic system involving a Volterra kernel modelling an hereditarily-elastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of...

Mathematical challenges in shape optimization (2005)

Mathematical challenges in shape optimization (2005)

This paper covers some theoretical investigations performed in France, in the framework of the CNRS programme GDR {\it Applications Nouvelles de l'Optimisation de Forme}. The programme included also...

Mathematical challenges in shape optimization (2005)

This paper covers some theoretical investigations performed in France, in the framework of the CNRS programme GDR {\it Applications Nouvelles de l'Optimisation de Forme}. The programme included also...

Mathematical challenges in shape optimization (2005)

This paper covers some theoretical investigations performed in France, in the framework of the CNRS programme GDR {\it Applications Nouvelles de l'Optimisation de Forme}. The programme included also...

On shape optimization for compressible isothermal Navier-Stokes equations (2004)

This paper covers some theoretical investigations performed in France, in the framework of the CNRS programme GDR {\it Applications Nouvelles de l'Optimisation de Forme}. The programme included also...

Plotnikov, P. I., Sokolowski, Jan

The steady state system of isothermal Navier-Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of drag minimisation with respect to the...

On shape optimization for compressible isothermal Navier-Stokes equations (2004)

Plotnikov, P. I., Sokolowski, Jan

The steady state system of isothermal Navier-Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of drag minimisation with respect to the...

On shape optimization for compressible isothermal Navier-Stokes equations (2004)

Plotnikov, P. I., Sokolowski, Jan

The steady state system of isothermal Navier-Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of drag minimisation with respect to the...

Asymptotic analysis of shape functionals (2002)

Asymptotic analysis of shape functionals (2002)

A family of boundary value problems is considered in domains $\Omega(\varepsilon)=\Omega\setminus\overline\omega_\varepsilon \subset\mathbb{R}^n$, $n\ge 3$, with cavities $\omega_\varepsilon$...

Asymptotic analysis of shape functionals (2002)

A family of boundary value problems is considered in domains $\Omega(\varepsilon)=\Omega\setminus\overline\omega_\varepsilon \subset\mathbb{R}^n$, $n\ge 3$, with cavities $\omega_\varepsilon$...

Optimal Shape Design of Inductor Coils for Surface Hardening (1999)

A family of boundary value problems is considered in domains $\Omega(\varepsilon)=\Omega\setminus\overline\omega_\varepsilon \subset\mathbb{R}^n$, $n\ge 3$, with cavities $\omega_\varepsilon$...

Topological Derivative for Nucleation of Non-Circular Voids (1999)

Nous considérons un problème d'optimisation de forme relatif à la modélisatio- n d'endurcissement par induction. Le modèle mathématique consiste en une formulation potentielle vectorielle...

Shape Sensitivity Analysis of Variational Problems in Domains with Cracks (1999)

The hitherto existing literature concerning the topological derivative of shape functionals concerned perturbations of domains caused by introduction of circular or ball openings. In the present...

Fremiot, Gilles, Sokolowski, Jan

We obtain the structure theorem for a differentiable shape functional defined in a domain including curved cracks. The theorem is an extension of the structure theorem given eg. in [15] in the case...

The Topological Derivative Method and Artificial Neural Networks for Numerical Solution of Shape Inverse Problems (1999)

Jackowska-Strumillo, Lidia, Sokolowski, Jan, Zochowski, Antoni

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is...

Optimal Shape Design of Inductor Coils for Surface Hardening (1999)

Topological Derivative for Nucleation of Non-Circular Voids (1999)

Nous considérons un problème d'optimisation de forme relatif à la modélisation d'endurcissement par induction. Le modèle mathématique consiste en une formulation potentielle vectorielle pour...

Shape Sensitivity Analysis of Variational Problems in Domains with Cracks (1999)

The hitherto existing literature concerning the topological derivative of shape functionals concerned perturbations of domains caused by introduction of circular or ball openings. In the present...

Fremiot, Gilles, Sokolowski, Jan

We obtain the structure theorem for a differentiable shape functional defined in a domain including curved cracks. The theorem is an extension of the structure theorem given eg. in [15] in the case...

The Topological Derivative Method and Artificial Neural Networks for Numerical Solution of Shape Inverse Problems (1999)

Jackowska-Strumillo, Lidia, Sokolowski, Jan, Zochowski, Antoni

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is...

Optimal Shape Design of Inductor Coils for Surface Hardening (1999)

Topological Derivative for Nucleation of Non-Circular Voids (1999)

Nous considérons un problème d'optimisation de forme relatif à la modélisation d'endurcissement par induction. Le modèle mathématique consiste en une formulation potentielle vectorielle pour...

Shape Sensitivity Analysis of Variational Problems in Domains with Cracks (1999)

The hitherto existing literature concerning the topological derivative of shape functionals concerned perturbations of domains caused by introduction of circular or ball openings. In the present...

Fremiot, Gilles, Sokolowski, Jan

We obtain the structure theorem for a differentiable shape functional defined in a domain including curved cracks. The theorem is an extension of the structure theorem given eg. in [15] in the case...

The Topological Derivative Method and Artificial Neural Networks for Numerical Solution of Shape Inverse Problems (1999)

Jackowska-Strumillo, Lidia, Sokolowski, Jan, Zochowski, Antoni

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is...

Optimal Shells Formed on a Sphere. The Topological Derivative Method (1998)

Griffith Formulae for Elasticity Systems with unilateral Conditions (1998)

The subject of the paper is the analysis of sensitivity of a thin elastic spherical shell to the change of its shape associated with forming a small circular opening, far from the loading applied....

Khludnev, Alexander M., Sokolowski, Jan

In the paper we consider the elasticity equations in nonsmooth domains in $R^n, n=2,3$. The domains have a crack whose length may change. At the crack faces, inequality type boundary conditions...

Optimal Shells Formed on a Sphere. The Topological Derivative Method (1998)

Griffith Formulae for Elasticity Systems with unilateral Conditions (1998)

The subject of the paper is the analysis of sensitivity of a thin elastic spherical shell to the change of its shape associated with forming a small circular opening, far from the loading applied....

Khludnev, Alexander M., Sokolowski, Jan

In the paper we consider the elasticity equations in nonsmooth domains in $R^n, n=2,3$. The domains have a crack whose length may change. At the crack faces, inequality type boundary conditions...

Optimal Shells Formed on a Sphere. The Topological Derivative Method (1998)

Griffith Formulae for Elasticity Systems with unilateral Conditions (1998)

The subject of the paper is the analysis of sensitivity of a thin elastic spherical shell to the change of its shape associated with forming a small circular opening, far from the loading applied....

Khludnev, Alexander M., Sokolowski, Jan

In the paper we consider the elasticity equations in nonsmooth domains in $R^n, n=2,3$. The domains have a crack whose length may change. At the crack faces, inequality type boundary conditions...

Optimal Boundary Control Problems For Shape Memory Alloys Under State Constraints For Stress And Temperature (1998)

Nikolaus Bubner, Jan Sokolowski, Jürgen Sprekels

We consider two optimal control problems for first order martensitic phase transitions in a deformation--driven experiment on shape memory alloys including state constraints for the total stress and...

Tangent Cones in Besov Spaces (1997)

Shape Optimization Problem for Heat Equation (1997)

Tangent cones for obstacle problem arise when studying differentiability of metric projection. Characterising the tangent cones is the first step in these considerations. This has been done in some...

Calculating tangent sets to certain sets in functional spaces (1997)

In this paper the support of a Radon measure is selected in an optimal way. The solution of the parabolic equation depends on the mesure via the mixed type boundary conditions. The existence of a...

Bednarczuk, Ewa, Pierre, Michel, Rouy, Elisabeth, Sokolowski, Jan

We give necessary and sufficient conditions for a given element to be a member of the second order tangent set $T»_{K}(f,v)$ to the positive cone $K$ in $L^{\infty}¸.$ Since, in general...

On Solvability of Boundary Value Problems in Elastoplasticity (1997)

Khludnev, Alexander, Sokolowski, Jan

In the paper the existence of a solution to the three dimensional elastoplastic problem with the Prandtl-Reuss constitutive law and the Neumann boundary conditions is obtained. The proof is based on...

On Topological Derivative in Shape Optimization (1997)

We present a mathematical model for the laser surface hardening of steel. It consists of a nonlinear heat equation coupled with a system of five ordinary differential equations to describe the volume...

Tangent Cones in Besov Spaces (1997)

In the paper the topological derivative for arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system in the plane. The topological derivative can...

Shape Optimization Problem for Heat Equation (1997)

Tangent cones for obstacle problem arise when studying differentiability of metric projection. Characterising the tangent cones is the first step in these considerations. This has been done in some...

Calculating tangent sets to certain sets in functional spaces (1997)

In this paper the support of a Radon measure is selected in an optimal way. The solution of the parabolic equation depends on the mesure via the mixed type boundary conditions. The existence of a...

Bednarczuk, Ewa, Pierre, Michel, Rouy, Elisabeth, Sokolowski, Jan

We give necessary and sufficient conditions for a given element to be a member of the second order tangent set $T»_{K}(f,v)$ to the positive cone $K$ in $L^{\infty}¸.$ Since, in general...

On Solvability of Boundary Value Problems in Elastoplasticity (1997)

Khludnev, Alexander, Sokolowski, Jan

In the paper the existence of a solution to the three dimensional elastoplastic problem with the Prandtl-Reuss constitutive law and the Neumann boundary conditions is obtained. The proof is based on...

On Topological Derivative in Shape Optimization (1997)

We present a mathematical model for the laser surface hardening of steel. It consists of a nonlinear heat equation coupled with a system of five ordinary differential equations to describe the volume...

Tangent Cones in Besov Spaces (1997)

In the paper the topological derivative for arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system in the plane. The topological derivative can...

Shape Optimization Problem for Heat Equation (1997)

Tangent cones for obstacle problem arise when studying differentiability of metric projection. Characterising the tangent cones is the first step in these considerations. This has been done in some...

Calculating tangent sets to certain sets in functional spaces (1997)

In this paper the support of a Radon measure is selected in an optimal way. The solution of the parabolic equation depends on the mesure via the mixed type boundary conditions. The existence of a...

Bednarczuk, Ewa, Pierre, Michel, Rouy, Elisabeth, Sokolowski, Jan

We give necessary and sufficient conditions for a given element to be a member of the second order tangent set $T»_{K}(f,v)$ to the positive cone $K$ in $L^{\infty}¸.$ Since, in general...

On Solvability of Boundary Value Problems in Elastoplasticity (1997)

Khludnev, Alexander, Sokolowski, Jan

In the paper the existence of a solution to the three dimensional elastoplastic problem with the Prandtl-Reuss constitutive law and the Neumann boundary conditions is obtained. The proof is based on...

On Topological Derivative in Shape Optimization (1997)

We present a mathematical model for the laser surface hardening of steel. It consists of a nonlinear heat equation coupled with a system of five ordinary differential equations to describe the volume...

In the paper the topological derivative for arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system in the plane. The topological derivative can...

Dietmar Hömberg, Jan Sokolowski, Projet Numath

We present a mathematical model for the laser surface hardening of steel. It consists of a nonlinear heat equation coupled with a system of five ordinary differential equations to describe the volume...

Shape Optimization Problem for Heat Equation (1997)

Antoine Henrot, Jan Sokolowski

: In this paper the support of a Radon measure is selected in an optimal way. The solution of the parabolic equation depends on the mesure via the mixed type boundary conditions. The existence of a...

Boundary Control Problems for Shape Memory Alloys under State Constraints (1996)

Bubner, Nikolaus, Sokolowski, Jan, Sprekels, Jürgen

We consider two optimal control problems for first order martensitic phase transitions in a deformation--driven experiment on shape memory alloys including state constraints for the total stress and...

Displacement Derivatives in Shape Optimization of Thin Shells (1996)

Domain Optimization Problem for Stationary Heat Equation (1996)

In the present paper the framework for the shape sensitivity analysis of systems of equations defined on a surface in $\bbbr^3$ is established. The model of thin shell presented in Koiter, 1970 is...

Henrot, Antoine, Horn, Werner, Sokolowski, Jan

In the paper the support of a Radon measure is selected in an optimal way. The solution of the second order elliptic equation depends on the mesure via the mixed type boundary conditions. The...

Boundary Control Problems for Shape Memory Alloys under State Constraints (1996)

Bubner, Nikolaus, Sokolowski, Jan, Sprekels, Jürgen

We consider two optimal control problems for first order martensitic phase transitions in a deformation--driven experiment on shape memory alloys including state constraints for the total stress and...

Displacement Derivatives in Shape Optimization of Thin Shells (1996)

Domain Optimization Problem for Stationary Heat Equation (1996)

In the present paper the framework for the shape sensitivity analysis of systems of equations defined on a surface in $\bbbr^3$ is established. The model of thin shell presented in Koiter, 1970 is...

Henrot, Antoine, Horn, Werner, Sokolowski, Jan

In the paper the support of a Radon measure is selected in an optimal way. The solution of the second order elliptic equation depends on the mesure via the mixed type boundary conditions. The...

Boundary Control Problems for Shape Memory Alloys under State Constraints (1996)

Bubner, Nikolaus, Sokolowski, Jan, Sprekels, Jürgen

We consider two optimal control problems for first order martensitic phase transitions in a deformation--driven experiment on shape memory alloys including state constraints for the total stress and...

Displacement Derivatives in Shape Optimization of Thin Shells (1996)

Domain Optimization Problem for Stationary Heat Equation (1996)

In the present paper the framework for the shape sensitivity analysis of systems of equations defined on a surface in $\bbbr^3$ is established. The model of thin shell presented in Koiter, 1970 is...

Henrot, Antoine, Horn, Werner, Sokolowski, Jan

In the paper the support of a Radon measure is selected in an optimal way. The solution of the second order elliptic equation depends on the mesure via the mixed type boundary conditions. The...

Domain Optimization Problem for Stationary Heat Equation (1996)

Antoine Henrot, Werner Horn, Jan Sokolowski, Projet Numath

In the paper the support of a Radon measure is selected in an optimal way. The solution of the second order elliptic equation depends on the mesure via the mixed type boundary conditions. The...

Boundary Control Problems for Shape Memory Alloys under State Constraints (1996)

Jürgen Sprekels, Jan Sokolowski, Nikolaus Bubner, Nikolaus Bubner, Projet Numath

: We consider two optimal control problems for rst order martensitic phase transitions in a deformationdriven experiment on shape memory alloys including state constraints for the total stress and...

Control Problems with State Constraints for the Penrose-Fife Phase-field model (1995)

Horn, Werner, Sokolowski, Jan, Sprekels, Jürgen

Control Problems with State Constraints for the Penrose-Fife Phase-field model (1995)

Horn, Werner, Sokolowski, Jan, Sprekels, Jürgen

This article gives an optimality system for a control problem with state constraints for a Penrose-Fife model for phase transitions.

Control Problems with State Constraints for the Penrose-Fife Phase-field model (1995)

Horn, Werner, Sokolowski, Jan, Sprekels, Jürgen

This article gives an optimality system for a control problem with state constraints for a Penrose-Fife model for phase transitions.

Control Problems with State Constraints for the Penrose-Fife Phase-field model (1995)

Jürgen Sprekels, Jan Sokolowski, Werner Horn, Werner Horn, Projet Numath

: This article gives an optimality system for a control problem with state constraints for a Penrose-Fife model for phase transitions. Key-words: state constraints, optimality system, phase...

Control Problems with State Constraints for the Penrose-Fife Phase-Field Model (1995)

Jan Sokolowski, Werner Horn, Werner Horn, Jürgen Sprekels, Jurgen Sprekels

This article gives an optimality system for a control problem with state constraints for a Penrose-Fife model for phase transitions. 1 Introduction In this article, we consider optimal control...

Directional differentiability of metric projection in [..] and applications (1992)

Directional differentiability of metric projection in [..] and applications (1992)

The form of directional derivative of the metric projection in the Sobolev space HS(2;0)() into the convex set K = {f HS(2;0)() | f y } is derived. The result is used to obtain the differential...

Directional differentiability of metric projection in [..] and applications (1992)

The form of directional derivative of the metric projection in the Sobolev space HS(2;0)() into the convex set K = {f HS(2;0)() | f y } is derived. The result is used to obtain the differential...

sensitivity analysis of Kirchhof plate with obstacle (1987)

The form of directional derivative of the metric projection in the Sobolev space HS(2;0)() into the convex set K = {f HS(2;0)() | f y } is derived. The result is used to obtain the differential...

sensitivity analysis of Kirchhof plate with obstacle (1987)

sensitivity analysis of Kirchhof plate with obstacle (1987)

Differential stability of solutions to constrained optimization problems (1984)

Differential stability of solutions to constrained optimization problems (1984)

Differential stability of solutions to constrained optimization problems (1984)