On the sharp regularity of solutions to hyperbolic boundary value problems

2022/06/27 by Corentin Audiard, Audiard, Corentin
Mathematics · Engineering · #Differential Equations and Boundary Problems #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.13293

Abstract

We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and regularity in fractional Sobolev spaces. This last point is specially interesting when the regularity index belongs to 1/2 + N, as it involves nonlocal compatibility conditions.

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