A construction of representing measures for elliptic and parabolic differential equations

DOI10.1007/BF01475753zbMath0469.31010MaRDI QIDQ1156909

Peter A. Loeb

Publication date: 1982

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

Full work available at URL: https://eudml.org/doc/163654

zbMATH Keywords

positive harmonic functionsBrelot harmonic spacemaximal representing measuresBauer harmonic spacestandard- analysis constructionuniversal nets

Mathematics Subject Classification ID

Axiomatic potential theory (31D05) Probabilistic potential theory (60J45) Connections of harmonic functions with differential equations in higher dimensions (31B35)

Related Items (2)

Representing measures in potential theory and an ideal boundary ⋮ An intuitive approach to the Martin boundary

Cites Work

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• A regular metrizable boundary for solutions of elliptic and parabolic differential equations
• Applications of nonstandard analysis to ideal boundaries in potential theory
• Sandwich theorems and lattice semigroups
• The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot
• Harmonic spaces and their potential theory
• An axiomatic treatment of pairs of elliptic differential equations
• On topologies and boundaries in potential theory. Enlarged ed. of a course of lectures delivered in 1966
• A Generalization of the Riesz-Herglotz Theorem on Representing Measures
• Positive Harmonic Functions on Lipschitz Domains
• Minimal Positive Harmonic Functions
• Non-standard analysis

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