On the limit Sobolev regularity for Dirichlet and Neumann problems on Lipschitz domains
Martin Costabel · Mathematische Nachrichten · 2019
Abstract We construct a bounded C 1 domain Ω in for which the regularity for the Dirichlet and Neumann problems for the Laplacian cannot be improved, that is, there exists f in such that the solution of in Ω and either on or on is contained in but not in for any . An analogous result holds for Sobolev spaces with .