IUMJ

Title: Higher regularity in the classical layer potential theory for Lipschitz domains

Authors: Vladimir Maz'ya and Tatyana Shaposhnikova

Issue: Volume 54 (2005), Issue 1, 99-142

Abstract:

Classical boundary integral equations of the harmonic potential theory on Lipschitz surfaces are studied. We obtain higher fractional Sobolev regularity results for their solutions under sharp conditions on the surface. These results are derived from a theorem on the solvability of auxiliary boundary value problems for the Laplace equation in weighted Sobolev spaces.