Harmonic polynomials and tangent measures of harmonic measure

Badger, Matthew

doi:10.4171/RMI/654

Revista Matemática Iberoamericana

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Volume 27, Issue 3, 2011, pp. 841–870

DOI: 10.4171/RMI/654

Published online: 2011-12-06

Harmonic polynomials and tangent measures of harmonic measure

Matthew Badger^[1]

(1) University of Washington, Seattle, USA

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.

Keywords: Harmonic measure, tangent measures, spherical harmonics

Badger Matthew: Harmonic polynomials and tangent measures of harmonic measure. Rev. Mat. Iberoam. 27 (2011), 841-870. doi: 10.4171/RMI/654