A Thomson's principle and a Rayleigh's monotonicity law for nonlinear networks

DOI10.1007/s11118-016-9562-1zbMath1353.31007OpenAlexW2395099982MaRDI QIDQ345033

Atsushi Kasue

Publication date: 25 November 2016

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

Full work available at URL: https://doi.org/10.1007/s11118-016-9562-1

zbMATH Keywords

potential theory on networksRayleigh's monotonicity lawThomson's principle

Mathematics Subject Classification ID

Discrete potential theory (31C20) Infinite graphs (05C63)

Related Items

Unnamed Item ⋮ Resolutive ideal boundaries of nonlinear resistive networks ⋮ Some function theoretic properties of nonlinear resistive networks

Cites Work

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• Global comparison principles for the \(p\)-Laplace operator on Riemannian manifolds
• Boundary limit of discrete Dirichlet potentials
• Denumerable Markov chains. Generating functions, boundary theory, random walks on trees.
• Ideal boundary limit of discrete Dirichlet functions
• The extremal length of a network
• Generalized extremal length of an infinite network
• Parabolic and hyperbolic infinite networks
• Approximation of currents in infinite nonlinear resistive networks
• Morphisms and currents in infinite nonlinear resistive networks
• Potential theory on infinite networks
• \(p\)-harmonic functions on graphs and manifolds
• The Kelvin-Nevanlinna-Royden criterion for \(p\)-parabolicity
• Martin and End Compactifications for Nonlocally Finite Graphs
• A Thomson's Principle for Infinite, Nonlinear Resistive Networks
• Infinite Electrical Networks
• LACK OF SPHERE PACKING OF GRAPHS VIA NONLINEAR POTENTIAL THEORY
• EXPANSION CONSTANTS AND HYPERBOLIC EMBEDDINGS OF FINITE GRAPHS
• Infinite networks: I--Resistive networks
• Harmonic functions on planar and almost planar graphs and manifolds, via circle packings