Harmonic polynomials and tangent measures of harmonic measure

Details Harmonic polynomials and tangent measures of harmonic measure Harmonic polynomials and tangent measures of harmonic measure

2009-10-14

arxiv.org/abs/0910.2591v1

Rev. Mat. Iberoamericana 27 (2011), no. 3, 841--870

Mathematics

Analysis of PDEs

23 pages, 1 figure

Scientific paper

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.

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