On the characterization of harmonic and subharmonic functions via mean-value properties

DOI10.1007/s11118-009-9150-8zbMath1187.31003arXivmath/0106078OpenAlexW2080763162MaRDI QIDQ849295

Pedro Freitas, João Palhoto Matos

Publication date: 25 February 2010

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

Full work available at URL: https://arxiv.org/abs/math/0106078

zbMATH Keywords

harmonic functionsubharmonic functionmean value

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

Related Items (13)

Global boundedness of functions of finite order that are bounded outside small sets ⋮ Optimal general Hermite-Hadamard-type inequalities in a ball and their applications in multidimensional numerical integration ⋮ The logarithm of the modulus of a holomorphic function as a minorant for a subharmonic function. II: The complex plane ⋮ The Logarithm of the Modulus of an Entire Function as a Minorant for a Subharmonic Function outside a Small Exceptional Set ⋮ On Hermite-Hadamard-Type Inequalities for Subharmonic Functions Over Circular Ring Domains ⋮ Subharmonic functions in sub-Riemannian settings ⋮ On relations between harmonic and panharmonic functions ⋮ On the mean value property of fractional harmonic functions ⋮ Blaschke, Privaloff, Reade and Saks theorems for diffusion equations on Lie groups ⋮ A characterization of harmonic functions by quadrature identities on annular domains and related results ⋮ Panharmonic functions: mean value properties and related topics ⋮ Mean value properties of harmonic functions and related topics (a survey) ⋮ Necessary and sufficient conditions for zero subsets of holomorphic functions with upper constraints in planar domains

Cites Work

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• On the mean-value property of harmonic functions
• A symmetry problem in potential theory
• Regular solids and harmonic polynomials
• Some remarks on subharmonic functions
• Duality theorems in some overdetermined boundary value problems
• Integral Harnack inequality
• Symmetry in an Overdetermined Fourth Order Elliptic Boundary Value Problem
• The volume mean-value property of harmonic functions
• Subharmonic Functions and Surfaces of Negative Curvature
• On the Mean-Value Property of Harmonic Functions

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