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arXiv · 1409.4460

A Two-Phase Free Boundary Problem for Harmonic Measure

Max Engelstein
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Abstract

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro and prove a sharp H\"older 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.

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Max Engelstein. 2014-09-15. A Two-Phase Free Boundary Problem for Harmonic Measure. https://arxiv.org/abs/1409.4460

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