A pseudo-extractor approach to hidden boundary regularity for the wave equation with mixed boundary conditions

Abstract

In this paper we introduce a new approach to “hidden” boundary regularity for the linear wave equation with mixed Dirichlet–Neumann boundary conditions, where the Neumann data is non-smooth. First, we obtain existence and uniqueness of solution by Galerkin estimates. Then we use a new, pseudo-extractor technique (based on the Fourier transform and shape and tangential calculus) in order to provide sharp regularity for the solution at the boundary.