Revista Matemática Iberoamericana

Harmonic polynomials and tangent measures of harmonic measure

Matthew Badger

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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.

Article information

Source
Rev. Mat. Iberoamericana Volume 27, Number 3 (2011), 841-870.

Dates
First available in Project Euclid: 9 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1312906779

Mathematical Reviews number (MathSciNet)
MR2895335

Zentralblatt MATH identifier
1242.28003

Subjects
Primary: 28A33: Spaces of measures, convergence of measures [See also 46E27, 60Bxx] 31A15: Potentials and capacity, harmonic measure, extremal length [See also 30C85] 33C55: Spherical harmonics

Keywords
harmonic measure tangent measures spherical harmonics

Citation

Badger , Matthew. Harmonic polynomials and tangent measures of harmonic measure. Rev. Mat. Iberoamericana 27 (2011), no. 3, 841--870. https://projecteuclid.org/euclid.rmi/1312906779.


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