Virial identity and weak dispersion for the magnetic Dirac equation (2009)
Boussaid, Nabile, D'Ancona, Piero, Fanelli, Luca
We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates...
Endpoint Strichartz estimates for the magnetic Schrodinger equation (2009)
D'Ancona, Piero, Fanelli, Luca, Vega, Luis, Visciglia, Nicola
We prove Strichartz estimates for the Schroedinger equation with an electromagnetic potential, in dimension $n\geq3$. The decay and regularity assumptions on the potentials are almost critical, i.e.,...
Virial identity and weak dispersion for the magnetic Dirac equation (2009)
Boussaid, Nabile, D'Ancona, Piero, Fanelli, Luca
We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates...
Virial identity and weak dispersion for the magnetic Dirac equation (2009)
Boussaid, Nabile, D'Ancona, Piero, Fanelli, Luca
We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates...
Smoothing estimates for the Schrodinger equation with unbounded potentials (2008)
D'Ancona, Piero, Fanelli, Luca
We prove a local in time smoothing estimate for a magnetic Schrodinger equation with coefficients growing polynomially at spatial infinity. The assumptions on the magnetic field are gauge invariant...
Null structure and almost optimal local well-posedness of the Maxwell-Dirac system (2008)
D'Ancona, Piero, Foschi, Damiano, Selberg, Sigmund
We uncover the full null structure of the Maxwell-Dirac system in Lorenz gauge. This structure, which cannot be seen in the individual component equations, but only when considering the system as a...
Strichartz and smoothing estimates for dispersive equations with magnetic potentials (2007)
D'Ancona, Piero, Fanelli, Luca
We prove global smoothing and Strichartz estimates for the Schroedinger, wave, Klein-Gordon equations and for the massless and massive Dirac systems, perturbed with singular electromagnetic...
D'Ancona, Piero, Foschi, Damiano, Selberg, Sigmund
We prove that the Cauchy problem for the Dirac-Klein-Gordon equations in two space dimensions is locally well-posed in a range of Sobolev spaces of negative index for the Dirac spinor, and an...
Dispersive estimate for the Schroedinger equation with point interactions (2005)
D'Ancona, Piero, Pierfelice, Vittoria, Teta, Alessandro
We consider the Schroedinger operator in R^3 with N point interactions placed at Y=(y_1, ... ,y_N), y_j in R^3, of strength a=(a_1, ... ,a_N). Exploiting the spectral theorem and the rather explicit...
L^p boundedness of the wave operator for the one dimensional Schroedinger operator (2005)
D'Ancona, Piero, Fanelli, Luca
Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> \pm\infty of the operators e^{isH}...
Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system (2005)
D'Ancona, Piero, Foschi, Damiano, Selberg, Sigmund
We prove almost optimal local well-posedness for the coupled Dirac-Klein-Gordon (DKG) system of equations in 1+3 dimensions. The proof relies on the null structure of the system, combined with...
Decay estimates for the wave and Dirac equations with a magnetic potential (2005)
D'Ancona, Piero, Fanelli, Luca
We study the dispersive properties of the wave equation and the massless Dirac equation in three space dimensions, perturbed with electromagnetic potentials. The potentials are assumed to be small...
Some remarks on the Schr\"odinger equation with a potential in $L^{r}_{t}L^{s}_{x}$ (2005)
D'Ancona, Piero, Pierfelice, Vittoria, Visciglia, Nicola
We study the dispersive properties of the linear Schr\"odinger equation with a time-dependent potential $V(t,x)$. We show that an appropriate integrability condition in space and time on $V$, i.e....
On the wave equation with a large rough potential (2003)
D'Ancona, Piero, Pierfelice, Vittoria
We prove an optimal dispersive $L^{\infty}$ decay estimate for a three dimensional wave equation perturbed with a large non smooth potential belonging to a particular Kato class. The proof is based...
On the Continuity of the Solution Operator to the Wave Map System (2003)
Piero D'Ancona, Vladimir Georgiev
We investigate the continuity properties of the solution operator to the wave map system from general nonflat target of arbitrary dimension, and we prove by an explicit class of counterexamples that...
Low Regularity Solutions For The Wave Map Equation Into The 2-D Sphere (2003)
Piero D'Ancona, Vladimir Georgiev
A class of weak wave map solutions with initial data in Sobolev space of order s < 1 is studied. A non uniqueness result is proved for the case, when the target manifold is a two dimensional...
On the continuity of the solution operator to the wave map system (2002)
D'Ancona, Piero, Georgiev, Vladimir
We investigate the continuity properties of the solution operator to the wave map system from the flat Minkowski space to a general nonflat target of arbitrary dimension, and we prove by an explicit...
Weakly Hyberbolic Equations in Domains with Boundaries (1996)
D'Ancona, Piero, Racke, Reinhard
We consider weakly hyperbolic equations of the type utt(t)+a(t)Au(t)=f(t,u(t)), u(0)=u0, ut(0)=u1, u(t) in D(A), t in [0,T], for a function u:[0,T]->H, T a nonnegative real, H a separable Hilbert...