Martin boundary of a fractal domain

DOI10.1023/A:1021823023212zbMath1021.31002OpenAlexW1538341322MaRDI QIDQ1868140

Tomohiko Mizutani, Hiroaki Aikawa, Torbjörn Lundh

Publication date: 27 April 2003

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1021823023212

zbMATH Keywords

Martin boundaryGreen functionboundary Harnack principlefractalinternal metricuniformly John domain

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Martin boundary theory (31C35) Boundary behavior of harmonic functions in higher dimensions (31B25)

Related Items (12)

Scale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces ⋮ Scale-invariant boundary Harnack principle in inner uniform domains ⋮ Doubling conditions for harmonic measure in John domains ⋮ Boundary estimates for superharmonic functions and solutions of semilinear elliptic equations with source ⋮ Potential theory on minimal hypersurfaces. I: Singularities as Martin boundaries ⋮ A quasi-linear Neumann problem of Ambrosetti-Prodi type on extension domains ⋮ Boundaries of planar graphs, via circle packings ⋮ Quasisymmetric conjugacy between quadratic dynamics and iterated function systems ⋮ Boundary Harnack principle and elliptic Harnack inequality ⋮ The Dirichlet heat kernel in inner uniform domains in fractal-type spaces ⋮ Global regularity for a class of quasi-linear local and nonlocal elliptic equations on extension domains ⋮ Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries

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