Wiener criterion for nonlocal Dirichlet problems / Regularity for nonlocal problems with non-standard growth

MK: In this talk, we study the boundary behavior of solutions to the Dirichlet problems for nonlocal nonlinear operators. We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the nonlocal nonlinear potential theory. This talk is based on a joint work with Ki-Ahm Lee and Se-Chan Lee.

MW: In this talk, we study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of (p,q)-type. Our main focus is on Hölder regularity estimates and full Harnack inequalities. Moreover, our results apply to weak solutions to a related class of nonlocal equations. This talk is based on joint works with Jamil Chaker and Minhyun Kim.