The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary

Abstract

We establish well posedness of the Dirichlet problem in weak local John domains $Ω\subset\R^\dmn$ with Ahlfors regular boundaries of possibly non integer dimension $0<\bdmn<\dmn$, for linear second order elliptic equations with real coefficients, and with data in Besov spaces with a very broad range of acceptable parameters.

30 pages, 2 figures