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arxiv: 1408.6789 · v1 · pith:TDR3OTCOnew · submitted 2014-08-28 · 🧮 math.AP

Wiener criterion for X-elliptic operators

classification 🧮 math.AP
keywords criterionoperatorsregularitywienerboundarycapacitarycharacterizationscondition
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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.

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