Related papers: The Kato Smoothing Effect for Regularized Schr\"od…

In this paper we prove the smoothing effect for solutions of Schr{\"o}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials at infinity.

In this work we consider an example of a linear time-degenerate Schr\"odinger operator. We show that with the appropriate assumptions the operator satisfies a Kato smoothing effect. We also show that the solutions to the nonlinear initial…

We prove that the geometric control condition is not necessary to obtain the smoothing effect and the uniform stabilization for the strongly dissipative Schr\"odinger equation.

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)…

In this expository note, we prove some extensions and refinements of classical Kato type estimates with elementary techniques.

We establish the Kato-type smoothing property, i.e., global-in-time smoothing estimates with homogeneous weights, for the Schr\"odinger equation on Riemannian symmetric spaces of non-compact type and general rank. These form a rich class of…

We are interested in this article in investigating the smoothing effect properties of the solutions of the Schrodinger equation. We deduce global well-posedness results for the cubic Schrodinger equation in the exterior of several convex…

This paper applies Hermite function techniques to give elementary proofs of Kato type smoothing estimates for the Schr\"odinger equation with quadratic potential in R^n+1. This is equivalent to proving a uniform L^2(R^n) to L^2(R^n)…

The smoothing effect states that solutions to the Schr{\"o}dinger equation in the Euclidean space have, for almost-every time, a local-in-space improved regularity (gain of half a derivative in Sobolev spaces). In this note, we show that,…

The aim of this note is to extend recent results of Yajima-Zhang \cite{Y-Z1, Y-Z2} on the 1/2- smoothing effect for Schr\"odinger equation with potential growing at infinity faster than quadratically.

In this paper we show that the local Kato type smoothing estimates are essentially equivalent to the global Kato type smoothing estimates for some class of dispersive equations including the Schr\"odinger equation. From this we immediately…

We consider refinements of the local smoothing estimates for the Schr\"odinger equation in domains which are exterior to a strictly convex obstacle in $\RR^n$. By restricting the solution to small, frequency dependent collars of the…

We analyze how the interaction between local and nonlocal dispersions, combined with different types of nonlinearities, influences the smoothing effects of solutions. To achieve this goal, we consider a model that generalizes the KdV and…

In this paper a global smoothing property of Schrodinger equations is established in the critical case in dimensions two and higher. It is shown that the critical smoothing estimate is attained if the smoothing operator has some structure.…

In this article, we study the decay of the solutions of Schr\"odinger equations in the exterior of an obstacle. The main situations we are interested in are the general case (no non-trapping assumptions) or some weakly trapping situations

Let \( H = (-\Delta)^m + V \) be a higher-order elliptic operator on \( L^2(\mathbb{R}^n) \), where \( V \) is a general bounded decaying potential. This paper focuses on the global Kato smoothing and Strichartz estimates for solutions to…

We prove that the quintic Schrodinger equation with Dirichlet boundary conditions is locally well posed for H^{1}_{0} data on any smooth, non-trapping domain of R^3. The key ingredient is a smoothing effect in L^{5}_{x}L^{2}_{t} for the…

In this paper, we prove that Kato smoothing effects for magnetic Schr\"odinger operators can yield the endpoint Strichartz estimates for linear wave equation with magnetic potential on two dimensional hyperbolic spaces. This result serves…

We prove resolvent estimates for a Schr\"odinger operator with a short-range potential outside an obstacle with Dirichlet boundary conditions. As a consequence, we deduce integrability of the local energy for the wave equation, and…

We prove smoothing properties and optimal Schauder type estimates for a class of nonautonomous evolution equations driven by time dependent Ornstein-Uhlenbeck operators in a separable Hilbert space. They arise as Kolmogorov equations of…