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Carlos Kenig, Tatiana Toro

Free boundary regularity below the continuous threshold: 2-phase problems

In the present paper we continue our study of free boundary regularity problems for harmonic measure and Poisson kernels, below the continuous threshold. We focus our attention on 2-phase problems. We show that under the appropriate hypothesis for the free boundary data, if each phase is geometrically non-degenerate then the free boundary is regular. The main new point of this work is that no flatness condition on the free boundary is assumed a priori.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 07/2006
Pages: 1 - 44

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