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C^{2,α}$ regularity of flat free boundaries for the thin one-phase problem
Published 10 Nov 2011 in math.AP | (1111.2513v1)
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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