Minhyun Kim

activity

20242026

collaborators

7 papers

math.AP2026

Capacities, Wiener criteria and fine continuity for nonlocal nonlinear equations

Anders Björn, Jana Björn, Minhyun Kim

In this paper we study nonlocal nonlinear equations of $s$ -fractional $p$ -Laplacian type in open subsets of $R^{n}$ . We investigate how the boundary regularity of solutions…

math.AP2026

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…

math.AP2026

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…

math.AP2025

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 $(s, p)$ -Laplacian type on $R^{n}$ . We show that the irregular boundary points for the Dirichlet problem can…

math.DG2025

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 $Ω ∖ K$ , where $Ω \subset R^{n}$ is an…

math.AP2024

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 $C^{s}$ boundary regularity for solutions to nonlocal elliptic equations with Hölder continuous coefficients in divergence form in $C^…