English

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

R2 v1 2026-06-22T05:57:25.213Z