A two-phase free boundary problem for harmonic measure

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Abstract

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro [21] and prove a sharp Hölder regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary condition. Thus we must establish non-degeneracy by means of monotonicity formulae.

Original languageEnglish (US)
Pages (from-to)859-905
Number of pages47
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume49
Issue number4
DOIs
StatePublished - Jul 1 2016
Externally publishedYes

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