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 Poincaré 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.
Wiener criterion for X-elliptic operators
Tralli Giulio
;
2015
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 Poincaré 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.
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