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

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

2011-11-10

arxiv.org/abs/1111.2513v1

Mathematics

Analysis of PDEs

Scientific paper

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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