Special Session 70: Progress and Challenges in Nonlocal and Nonhomogeneous PDEs

Wiener criterion for nonlocal and nonhomogeneous equations
Minhyun Kim
Hanyang University
Korea
Co-Author(s):    Ki-Ahm Lee, Se-Chan Lee
Abstract:
In this talk, we present the Wiener criterion for nonlocal equations with Orlicz growth, which provides a necessary and sufficient condition for boundary points to be regular. Our approach relies on the fine analysis of superharmonic functions in view of nonlocal nonlinear potential theory. Especially, the Wolff potential estimates play a fundamental role.