\(p\) harmonic measure in simply connected domains

DOI10.5802/aif.2626zbMath1241.35071arXiv0902.0013OpenAlexW2964334774MaRDI QIDQ646401

Kaj Nyström, Pietro Poggi-Corradini, John L. Lewis

Publication date: 17 November 2011

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.0013

zbMATH Keywords

Hausdorff dimension\(p\)-harmonic measure

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Nonlinear elliptic equations (35J60) Weak solutions to PDEs (35D30) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) PDEs with measure (35R06)

Related Items (7)

On a theorem of Wolff revisited ⋮ Hausdorff dimension and \(\sigma\) finiteness of \(p\) harmonic measures in space when \(p \geq n\) ⋮ The behavior at infinity of \(p\)-harmonic measure in an infinite slab ⋮ \(\sigma\)-finiteness of elliptic measures for quasilinear elliptic PDE in space ⋮ On the logarithm of the minimizing integrand for certain variational problems in two dimensions ⋮ The \(p\)-harmonic measure of small axially symmetric sets ⋮ 𝑝 harmonic measure in simply connected domains revisited

Cites Work

• Carleson type estimates for \(p\)-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces
• Boundary behavior and the Martin boundary problem for \(p\) harmonic functions in Lipschitz domains
• On the existence of a largest subharmonic minorant of a given function
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• Wolff snowflakes
• On the snow flake domain
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• On the dimension of harmonic measure of Cantor repellers
• Plane harmonic measures live on sets of \(\sigma\)-finite length
• On the Hausdorff dimension of harmonic measure in higher dimension
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• On the Makarov law of the iterated logarithm
• Boundary behaviour of p-harmonic functions in domains beyond Lipschitz domains
• On the Distortion of Boundary Sets Under Conformal Mappings
• On the support of harmonic measure for sets of Cantor type
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• Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains
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