Capacitary estimates for solutions to nonlocal Dirichlet problems
Minhyun Kim, Se-Chan Lee, Marvin Weidner
Abstract
We study the boundary regularity of weak solutions to nonlocal nonlinear elliptic equations with bounded measurable coefficients. Our main result establishes that a capacity density condition is equivalent to the validity of a uniform boundary Hölder estimate for solutions with Hölder continuous exterior data. More generally, we derive a fine capacitary estimate on the modulus of continuity that captures how regularity is inherited from the exterior datum to the solution.
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