Wiener criterion for X-elliptic operators

Abstract

In this note we prove a Wiener criterion of regularity of boundary points for the Dirichlet problem related to $X$-elliptic operators in divergence form enjoying the doubling condition and the Poincar\'e inequality. As a step towards this result, we exhibit some other characterizations of regularity in terms of the capacitary potentials. Finally, we also show that a cone-type criterion holds true in our setting.