The Kato Smoothing Effect for Regularized Schr\"odinger Equations in Exterior Domains

TL;DR

This paper establishes the Kato smoothing effect for solutions of inhomogeneous and damped Schrödinger equations in exterior domains, under specific geometric control conditions, advancing understanding of smoothing phenomena in such settings.

Contribution

It proves the Kato smoothing effect for Schrödinger equations in exterior domains with damping, under geometric control conditions, which was previously unestablished.

Findings

Kato smoothing effect holds under exterior geometric control.

Results apply to inhomogeneous and damped Schrödinger equations.

Advances understanding of smoothing in exterior domain PDEs.

Abstract

We prove, under the exterior geometric control condition, the Kato smoothing effect for solutions of an inhomogenous and damped Schr\"odinger equation on exterior domains.