Mean values and harmonic functions

DOI10.1007/BF01459494zbMath0794.31002MaRDI QIDQ1318000

Wolfhard Hansen, Nikolai S. Nadirashvili

Publication date: 23 March 1994

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

Full work available at URL: https://eudml.org/doc/165124

zbMATH Keywords

unbounded domainscontinuous \(h\)-bounded function

Mathematics Subject Classification ID

Brownian motion (60J65) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Martin boundary theory (31C35) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

Related Items (8)

Liouville's theorem and the restricted biharmonic mean value property on the plane ⋮ Harmonic functions on metric measure spaces ⋮ Polytopes and the mean value property ⋮ Liouville's theorem and the restricted biharmonic mean value property. ⋮ Mean value properties of harmonic functions and related topics (a survey) ⋮ Unnamed Item ⋮ Liouville's theorem and the restricted mean value property in the plane ⋮ On the restricted mean property for biharmonic functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces
• A converse to the mean value theorem for harmonic functions
• Potential theory. An analytic and probabilistic approach to balayage
• Perturbation by differences of unbounded potentials
• A zero-one law for a class of random walks and a converse to Gauss' mean value theorem
• Boundaries Induced by Non-negative Matrices
• On the Restricted Mean Value Property
• A Strong Converse to Gauss's Mean-Value Theorem
• A Converse to the Mean Value Theorem for Harmonic Functions
• Functions Having the Restricted Mean Value Property
• On Sufficient Conditions for Harmonicity
• Harmonic Functions and Mass Cancellation
• Converses of Gauss' Theorem on the Arithmetic Mean
• Ergodic Theory and Boundaries
• Restricted Mean Values and Harmonic Functions
• Functions Possessing Restricted Mean Value Properties
• On the “One-Circle” Problem for Harmonic Functions

This page was built for publication: Mean values and harmonic functions