Potential techniques and regularity of boundary value problems in exterior non-smooth domains - Regularity in exterior domains

摘要

Via Potential Theory, we obtain optimal solvability results in weighted Sobolev spaces for the Poisson's Problem for the Laplacian, with Dirichlet and Neumann boundary conditions in the exterior Omega of a bounded Lipschitz domain. As an application, we present suitable Helmholtz decompositions of vector fields defined on Omega. Our methods can be used to study similar regularity issues for systems.