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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2006, Issue 596, Pages 1–44, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2006.050, August 2006

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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.

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