A Wiener-type condition for Hölder continuity for Green's functions
The author studies local properties of the Green function of the complement of a compact set \(E\) in \(\mathbb R^d\), \(d>2\). A Wiener type characterization for the Hölder continuity of the Green function is given. The obtained density condition is necessary, and it is sufficient as well, provided \(E\) satisfies the cone condition. It is also shown that the Hölder condition for the Green function at a boundary point can be equivalently stated in terms of the equilibrium measure and the solution to the corresponding Dirichlet problem.
scientific article; zbMATH DE number 5082262