Higher regularity in the classical layer potential theory for Lipschitz domains
Vladimir Gilelevich Maz'ya, Tat'yana Olegovna Shaposhnikova · Indiana University Mathematics Journal · 2005
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.