We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro  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 language||English (US)|
|Number of pages||47|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - Jul 1 2016|