Regularity results for degenerate wave equations in a neighborhood of the boundary

TL;DR

This paper investigates the regularity of weak solutions to degenerate wave equations near boundaries, extending known results from nondegenerate cases and relating findings to boundary controllability.

Contribution

It provides new regularity results for degenerate wave equations near boundaries, building on and extending classical results for nondegenerate cases.

Findings

Regularity results for weak solutions near the boundary

Extension of classical nondegenerate results to degenerate cases

Implications for boundary controllability of wave equations

Abstract

In this paper we establish some regularity results concerning the behavior of weak solutions and very weak solutions of the degenerate wave equation near the boundary. For the nondegenerate case, the correponding results were originally obtained by Fabre and Puel (J. of Diff. Eq. 106, 1993). This kind of results is closely related to the exact boundary controllability for the wave equation as the limit of internal controllability.