Strichartz estimates without loss outside many strictly convex obstacles

TL;DR

This paper establishes lossless Strichartz estimates for Schrödinger and wave equations in the exterior of multiple strictly convex obstacles, extending previous results from two obstacles to finitely many.

Contribution

It generalizes prior work by proving Strichartz estimates without loss for multiple convex obstacles under Ikawa's condition.

Findings

Lossless Strichartz estimates for multiple obstacles

Extension from two to finitely many obstacles

Applicable to Schrödinger and wave equations

Abstract

We prove Strichartz estimates without loss for the Schr\"odinger equation and the wave equation outside finitely many strictly convex obstacles verifying Ikawa's condition, extending the approach we introduced previously for the two convex case.