On the sharp regularity of solutions to hyperbolic boundary value problems

TL;DR

This paper establishes precise regularity results for solutions to first-order hyperbolic boundary value problems, notably under weaker boundary data assumptions and in fractional Sobolev spaces, including nonlocal compatibility conditions.

Contribution

It introduces sharper regularity results with relaxed boundary data conditions and extends analysis to fractional Sobolev spaces for hyperbolic problems.

Findings

Weaker regularity assumptions on boundary data.

Regularity results in fractional Sobolev spaces.

Handling of nonlocal compatibility conditions for fractional indices.

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.