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

Speaker(s)

Minhyun Kim / Marvin Weidner

Affiliation

Universitaet Bielefeld

Date

Dec. 15, 2022, 12:30 p.m.

Room

room 5070

Seminar

Seminar of Mathematical Physics Equations Group

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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.

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