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arXiv · 1504.05569

Continuity and density results for a one-phase nonlocal free boundary problem

Serena Dipierro·Enrico Valdinoci
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Abstract

We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are H\"older continuous and the free boundary has positive density from both sides. For this, we also introduce a new notion of fractional harmonic replacement in the extended variables and we study its basic properties.

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Serena Dipierro, Enrico Valdinoci. 2015-04-21. Continuity and density results for a one-phase nonlocal free boundary problem. https://arxiv.org/abs/1504.05569

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