English

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}
}

Comments

35 pages

R2 v1 2026-06-28T08:00:27.061Z