This note characterizes boundary conditions for fractional harmonic extensions, suggesting Hölder regularity.
In this note, we characterize the sharp boundary condition such that the fractional harmonic extensions with Hölder regularity up to the boundary is globally Hölder continuous. The proofs are based on estimates of fractional harmonic measure decay and uniform fractional fatness of the complement of the domain.
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Feng Li (2025) studied this question.
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