6 papers
Capacitary estimates for solutions to nonlocal Dirichlet problems
Minhyun Kim, Se-Chan Lee, Marvin Weidner
We study the boundary regularity of weak solutions to nonlocal nonlinear elliptic equations with bounded measurable coefficients. Our main result establishes that a capacity densit…
Perron solutions and boundary regularity for nonlocal nonlinear Dirichlet problems
Anders Björn, Jana Björn, Minhyun Kim
For nonlinear operators of fractional \p-Laplace type, we consider two types of solutions to the nonlocal Dirichlet problem: Sobolev solutions based on fractional Sobolev spaces an…
Removable singularities for nonlocal minimal graphs
Minhyun Kim
We prove the removable singularity theorem for nonlocal minimal graphs. Specifically, we show that any nonlocal minimal graph in , where is…
Partial Hölder regularity for fully nonlinear nonlocal parabolic equations with integrable kernels
Minhyun Kim, Luke Schleef, Russell W. Schwab
In this work, we consider solutions to (fully nonlinear) parabolic integro-differential equations with integrable interaction kernels. A typical equation would be that obtained by…
Optimal boundary regularity and Green function estimates for nonlocal equations in divergence form
Minhyun Kim, Marvin Weidner
In this article we prove for the first time the boundary regularity for solutions to nonlocal elliptic equations with Hölder continuous coefficients in divergence form in $C…
Semiregular and strongly irregular boundary points for nonlocal Dirichlet problems
Anders Björn, Jana Björn, Minhyun Kim
In this paper we study nonlocal nonlinear equations of fractional -Laplacian type on . We show that the irregular boundary points for the Dirichlet problem can…