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

Daniela De Silva; Ovidiu Savin

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arXiv · 1111.2513

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

Daniela De Silva·Ovidiu Savin

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Abstract

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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Daniela De Silva, Ovidiu Savin. 2011-11-10. C^{2,\alpha}$ regularity of flat free boundaries for the thin one-phase problem. https://arxiv.org/abs/1111.2513

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