The Wiener criterion for elliptic equations with Orlicz growth

Abstract

We study the boundary continuity of solutions to elliptic equations with Orlicz growth. We first formulate the Wiener criterion which characterizes a regular boundary point by a geometric quantity coming from capacities. Secondly, we develop an estimate for the modulus of continuity at a boundary point, under a geometric condition on operators. The proof relies on capturing the local properties of weak solutions involving the Wolff potential estimate and the weak Harnack inequality.