A Two-Phase Free Boundary Problem for Harmonic Measure
Analysis of PDEs
2016-09-28 v2
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.
Keywords
Cite
@article{arxiv.1409.4460,
title = {A Two-Phase Free Boundary Problem for Harmonic Measure},
author = {Max Engelstein},
journal= {arXiv preprint arXiv:1409.4460},
year = {2016}
}
Comments
45 pages. This version has minor revisions as suggested by the referee