paper

Harmonic polynomials and tangent measures of harmonic measure

arXiv:0910.2591

Abstract

We show that on an NTA domain if each tangent measure to harmonic measure at a point is a polynomial harmonic measure then the associated polynomials are homogeneous. Geometric information for solutions of a two-phase free boundary problem studied by Kenig and Toro is derived.

23 pages, 1 figure