The Wiener criterion for fully nonlinear elliptic equations
Analysis of PDEs
2023-01-04 v1
Abstract
We study the boundary continuity of solutions to fully nonlinear elliptic equations. We first define a capacity for operators in non-divergence form and derive several capacitary estimates. Secondly, we formulate the Wiener criterion, which characterizes a regular boundary point via potential theory. Our approach utilizes the asymptotic behavior of homogeneous solutions, together with Harnack inequality and the comparison principle.
Keywords
Cite
@article{arxiv.2301.00960,
title = {The Wiener criterion for fully nonlinear elliptic equations},
author = {Ki-Ahm Lee and Se-Chan Lee},
journal= {arXiv preprint arXiv:2301.00960},
year = {2023}
}
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35 pages