A short proof of the H\"older-Poincar\'{e} Duality for $L_{p}$-cohomology (2009)
Gol'dshtein, Vladimir, Troyanov, Marc
We give a short proof of the duality theorem for the reduced $L_p$-cohomology of a complete oriented Riemannian manifold.
The H\"older-Poincar\'e Duality for $L_{q,p}$-cohomology (2009)
Gol'dshtein, Vladimir, Troyanov, Marc
We prove the following version of Poincare duality for reduced $L_{q,p}$-cohomology: For any $1
On the $L_{q,p}$-cohomology of Riemannian Manifolds with Negative Curvature (2008)
Gol'dshtein, Vladimir, Troyanov, Marc
We prove a non-vanishing result for the $L_{q,p}$-cohomology of complete simply-connected Riemannian manifolds with pinched negative curvature.
Distortion of Mappings and $L_{q,p}$-Cohomology (2008)
Gol'dshtein, Vladimir, Troyanov, Marc
We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$-cohomology of these manifolds. Some applications to vanishing and non...
On the naturality of the exterior differential (2008)
Gol'dshtein, Vladimir, Troyanov, Marc
We give sufficient conditions for the naturallity of the exterior differential under Sobolev mappings. In other words we study the validity of the equation $d f^* \alpha = f^* d\alpha$ for a smooth...
Lemma Poincar\'e for L_infty,loc - forms (2007)
Gol'dshtein, Vladimir, Dubrovskiy, Stanislav
We show that every closed L_infty,loc - form on R^n is exact. Differential is understood in the sense of currents. The proof does not use any explicit geometric constructions. De Rham theorem follows.
Multistability Control in Periodically Forced Catalytic Reactor (2007)
Vladimir Gol'dshtein, Vadim Panfilov
A novel approach of the chemical reactor stabilization is proposed by using a multistability control. A creation of an additional stable steady state by changing the reactor multiplicity features is...
Mediating Operation For A Simple Catalytic Reactor Model (2007)
Vladimir Gol'dshtein, Vadim Panfilov
INTRODUCTION A wide spectrum of multivariable dynamical systems can exhibit a rich dynamics characterized by different time scales. A periodic operation of intermediate mode with respect to slow and...
A Conformal de Rham Complex (2007)
Gol'dshtein, Vladimir, Troyanov, Marc
We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the...
Embedding Theorems and Boundary-value Problems for cusp domains (2007)
Gol'dshtein, Vladimir, Vasiltchik, Michail
We study the Robin boundary-value problem for bounded domains with isolated singularities. Because for such domains trace spaces of space $H^1(D)$ on its boundaries are weighted Sobolev spaces $L^{2,...
Sobolev inequalities for differential forms and $L_{q,p}$-cohomology. (2006)
Gol'dshtein, Vladimir, Troyanov, Marc
We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold $(M,g)$ and the $L_{q,p}$-cohomology of that manifold. The $L_{q,p}$-cohomology of $(M,g)$ is...
On a modified version of ILDM approach: asymptotic analysis based on integral manifolds (2006)
Bykov, Viatcheslav, Goldfarb, Igor, Gol'dshtein, Vladimir, Maas, Ulrich
Using the method of integral (invariant) manifolds, the intrinsic low-dimensional manifolds (ILDM) method is analysed. This is a method for identifying invariant manifolds of a system's slow dynamics...
Sobolev Inequalities for Differential Forms and $L_{q,p}$-cohomology (2005)
Gol'dshtein, Vladimir, Troyanov, Marc
We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold $(M,g)$ and the $L_{q,p}$-cohomology of that manifold. The $L_{q,p}$-cohomology of $(M,g)$ is...
On a modified version of ILDM approach: asymptotic analysis based on integral manifolds (2005)
Bykov, Viatcheslav, Goldfarb, Igor, Gol'dshtein, Vladimir, Maas, Ulrich
Using the method of integral (invariant) manifolds, the intrinsic low-dimensional manifolds (ILDM) method is analysed. This is a method for identifying invariant manifolds of a system's slow dynamics...
Some properties of hierarchic regular networks (a peep into fractal structures) (2004)
Surdutovich, Gregory, Gol'dshtein, Vladimir, Koganov, Gennady
We give exact relations for certain types of the hierarchic fractal structures. In the blatant distinction from regular networks of the "small world" (SW) topology [1], regular fractal networks...
Capacities in metric spaces. (2002)
Gol'dshtein, Vladimir, Troyanov, Marc
We discuss the potential theory related to variational capacity and the Sobolev capacity on metric measure spaces. We prove our results within the axiomatic framework.
An integral characterization of Hajlasz-Sobolev space. (2001)
Troyanov, Marc, Gol'dshtein, Vladimir
We prove that the pointwise inequality used by P. Hajlasz in his definition of Sobolev spaces on metric spaces is equivalent to an integral (Poincaré-type) inequality.
Axiomatic theory of Sobolev spaces. (2001)
Gol'dshtein, Vladimir, Troyanov, Marc
We develop an axiomatic approach to the theory of Sobolev spaces on metric measure spaces and we show that this axiomatic construction covers the main known examples (Hajlasz Sobolev spaces, weighted...
Compactness of the embedding operators for rough domains (2000)
Gol'dshtein, Vladimir, Ramm, Alexander G.
New classes of non-smooth bounded domains D, for which the embedding operator from H^1(D) into L^2(D) is compact are introduced. Examples are given and applications to scattering by rough obstacles...
The Kelvin-Nevanlinna-Royden criterion for $p$-parabolicity. (1999)
Gol'dshtein, Vladimir, Troyanov, Marc
We generalize the so called Kelvin–Nevanlinna–Royden crite- rion for the parabolicity of manifolds to the case of p-parabolicity for all p>1.
The $L_{pq}$-cohomology of SOL. (1998)
Gol'dshtein, Vladimir, Troyanov, Marc
It is proved that the second $L_{pq}$-cohomology of the Lie group SOL is infinite-dimensional.
Sur la non-résolubilité du $p$-laplacien sur $R^n$. (1998)
Gol'dshtein, Vladimir, Troyanov, Marc
In this note we prove the impossibility to solve the p-laplace equation $\Delta _p u + h = 0$ on $R^n$, $n \le p$ if the function $h$ has a non zero average.
Sur la non-résolubilité du p-laplacien sur R^n (1998)
Gol'dshtein, Vladimir, Troyanov, Marc
In this Note we prove the impossibility to solve the p-laplace equation Δpu + h = 0 on R^n, n ≤ p, if the function h has a non-zero average.
Mediating Operation of Heterogeneous CSTR (1996)
Vladimir Gol'dshtein, Vadim Panfilov, Isaak Shreiber
A new type of periodic operation is investigated for a simple model of a heterogeneous catalytic Continuous Stirred Tank Reactor (CSTR). For the heterogeneous case two scales of response times have...
Vladimir Gol'dshtein, Vadim Panfilov
A novel approach for stabilizing intermediate steady state of CSTR is proposed by using a special type of periodic forced operation, socalled mediating operation. Mediating operation enables to...