Fatou theorem of \(p\)-harmonic functions on trees.

DOI10.1214/aop/1019160328zbMath1038.31007OpenAlexW2009185127MaRDI QIDQ1872148

Robert P. Kaufman, Jang-Mei G. Wu

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1019160328

zbMATH Keywords

Fatou theoremfinite variation\(p\)-harmonic functionsdirected treefinite limit

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Discrete potential theory (31C20) Other generalizations (nonlinear potential theory, etc.) (31C45) Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions (31A20)

Related Items

Unnamed Item ⋮ NONLINEAR MEAN-VALUE FORMULAS ON FRACTAL SETS ⋮ Description of \(p\)-harmonic functions on the Cayley tree ⋮ Existence, uniqueness and decay rates for evolution equations on trees ⋮ Estimates for nonlinear harmonic measures on trees ⋮ The unique continuation property for a nonlinear equation on trees ⋮ Dirichlet-to-Neumann maps on trees ⋮ Description of periodic \(p\)-harmonic functions on Cayley tree ⋮ Convex envelopes on Trees

Cites Work

• Fatou theorems for some nonlinear elliptic equations
• On the radial variation of bounded analytic functions on the disc
• Gap series constructions for the \(p\)-Laplacian
• The radial variation of analytic functions
• On the fatou theorem for p-harmonic function
• About a fatou theorem for the _p-laplacian and related estimates for the hausdorff dimension of the support of certain l-harmonic measureS
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