Positive harmonic functions on non-tangentially accessible domains

DOI10.1007/BF01215142zbMath0555.31006MaRDI QIDQ760544

Rainer Wittmann

Publication date: 1985

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173637

zbMATH Keywords

Martin boundaryLaplace equationLipschitz domainsuniform Harnack inequalityBrelot harmonic spacetopological boundary

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) Martin boundary theory (31C35) Second-order elliptic equations (35J15) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)

Related Items (2)

Nicht-tangentiales Randverhalten von harmonischen Funktionen in irregulären Randpunkten. (Non-tangential boundary behaviour of harmonic functions in irregular boundary points) ⋮ Fatou and Littlewood related theorems and a convergence property in the R. S. Martin topology

Cites Work

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• On the Harnack inequality for linear elliptic equations
• On the existence of boundary values for harmonic functions in several variables
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• On the Martin compactification of a bounded Lipschitz domain in a Riemannian manifold
• Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
• On Harnack's theorem for elliptic differential equations
• On boundary Harnack principles and poles of extremal harmonic functions.
• Positive Harmonic Functions on Lipschitz Domains
• Minimal Positive Harmonic Functions

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