C^{2,\alpha}$ regularity of flat free boundaries for the thin one-phase problem

Daniela De Silva; Ovidiu Savin

arxiv: 1111.2513 · v1 · pith:TNQDVGTInew · submitted 2011-11-10 · 🧮 math.AP

C^(2,α) regularity of flat free boundaries for the thin one-phase problem

Daniela De Silva , Ovidiu Savin This is my paper

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keywords freeproblemone-phasealphaboundariesboundaryflatregularity

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We prove $C^{2,\alpha}$ regularity of sufficiently flat free boundaries, for the thin one-phase problem in which the free boundary occurs on a lower dimensional subspace. This problem appears also as a model of a one-phase free boundary problem in the context of the fractional Laplacian $(-\Delta)^{1/2}$.

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C^(2,α) regularity of flat free boundaries for the thin one-phase problem

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