Related papers: Strichartz estimates on exterior polygonal domains

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 and involve only the first two…

We show global-in-time Strichartz estimates for the isotropic Maxwell system with divergence free data. On the scalar permittivity and permeability we impose decay assumptions as $|x|\to\infty$ and a non-trapping condition. The proof is…

The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form $(-\Delta)^\alpha\partial_t u$, $\alpha\in(0,\frac{1}{2})$, in bounded smooth domains of $\Bbb R^3$. It appears that to…

We show the necessity of the non trapping condition for the plain smoothing effect ($H^{1/2}$) for Schr\"odinger equation with Dirichlet boundary conditions in exterior problems. We also give a class of trapped obstacles (Ikawa's example)…

We consider Maxwell equations on a smooth domain with perfectly conducting boundary conditions in isotropic media in two and three dimensions. In the charge-free case we recover Strichartz estimates due to Blair--Smith--Sogge for wave…

The present paper is concerned with Schr\"odinger equations with variable coefficients and unbounded electromagnetic potentials, where the kinetic energy part is a long-range perturbation of the flat Laplacian and the electric (resp.…

We prove the (local in time) Strichartz estimates (for the full range of parameters given by the scaling unless the end point) for asymptotically flat and non trapping perturbations of the flat Laplacian in $\R^n$, $n\geq 2$. The main point…

In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.

We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded…

We prove sharp Strichartz estimates for the semi-classical Schrodinger equation on a compact manifold with smooth, strictly geodesically concave boundary. We deduce sharp (classical) Strichartz estimates for the Schrodinger equation outside…

We consider an anisotropic model case for a strictly convex domain of dimension $d\geq 2$ with smoothboundary and we describe dispersion forthe semi-classical Schr{\"o}dinger equation with Dirichlet boundary condition. More specifically, we…

We prove wellposedness of the Cauchy problem for the nonlinear Schrodinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz…

We investigate new properties of the fractional Dirichlet Laplacian on smooth bounded domains and establish fractional product estimates and nonlinear Poincar\'e inequalities. We also use these tools to study the long-time dynamics of the…

In this article, we consider the focusing cubic nonlinear Schr\"odinger equation(NLS) in the exterior domain outside of a convex obstacle in $\mathbb{R}^3$ with Dirichlet boundary conditions. We revisit the scattering result below ground…

Doi proved that the $L^2_t H^{1/2}_x$ local smoothing effect for Schr\"odinger equation on a Riemannian manifold does not hold if the geodesic flow has one trapped trajectory. We show in contrast that Strichartz estimates and $L^1\to…

Local and global weighted norm estimates involving Muckenhoupt weights are obtained for gradient of solutions to linear elliptic Dirichlet boundary value problems in divergence form over a Lipschitz domain $\Omega$. The gradient estimates…

We prove global well-posedness of the two-dimensional exterior Navier-Stokes equations for bounded initial data with a finite Dirichlet integral, subject to the non-slip boundary condition. As an application, we construct global solutions…

We prove Strichartz estimates on general flat d-torus for arbitrary d. Using these estimates, we prove local wellposedness for the cubic nonlinear Schr\"odinger equations in appropriate Sobolev spaces. In dimensions 2 and 3, we prove…

We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such…

We prove smoothing estimates in Morrey-Campanato spaces for a Helmholtz equation $$ -Lu+zu=f, \qquad -Lu:=\nabla^{b}(a(x)\nabla^{b}u)-c(x)u, \qquad \nabla^{b}:=\nabla+ib(x) $$ with fully variable coefficients, of limited regularity, defined…