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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 -fractional -Laplacian type in open subsets of . 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…