The Poisson–Dirichlet problem in domains with Ahlfors regular boundary

Abstract

We present an announcement of some recent results concerning well-posedness of the Poisson–Dirichlet problem with boundary data in Besov spaces with fractional smoothness. This is a far-reaching generalization as previously known theorems concerning well-posedness of the Poisson problem in such intermediate smoothness classes were mostly restricted to the context of Lipschitz domains and coefficients satisfying strong regularity assumptions.