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

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