Classification of infinite networks and its application

DOI10.1007/BF01183152zbMath0769.94020OpenAlexW1994299578MaRDI QIDQ1207750

Maretsugu Yamasaki, Paolo M. Soardi

Publication date: 23 May 1993

Published in: Circuits, Systems, and Signal Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01183152

zbMATH Keywords

currentsvoltagediscrete Markov processesconstant Dirichlet finite \(p\)-harmonic functionsnonlinear infinite networks

Mathematics Subject Classification ID

Circuits, networks (94C99)

Related Items (10)

Infinite nonlinear resistive networks, after Minty ⋮ Density and trace results in generalized fractal networks ⋮ \(p\)-harmonic functions on graphs and manifolds ⋮ Parabolic theory of the discrete \(p\)-Laplace operator ⋮ A non-local quasi-linear ground state representation and criticality theory ⋮ Inequalities forp-superharmonic functions on networks ⋮ Topological groups and recurrence of quasi transitive graphs ⋮ Solving boundary value problems on networks using equilibrium measures ⋮ Rough Isometries and Dirichlet Finite Harmonic Functions on Graphs ⋮ Morphisms and currents in infinite nonlinear resistive networks

Cites Work

• Dirichlet norms, capacities and generalized isoperimetric inequalities for Markov operators.
• Isoperimetric inequalities and Markov chains
• Ideal boundary limit of discrete Dirichlet functions
• Parabolic and hyperbolic infinite networks
• Extremal length of an infinite network which is not necessarily locally finite
• Uniqueness of currents in infinite resistive networks
• Recurrence and transience of the edge graph of a tiling of the Euclidean plane
• A simple criterion for transience of a reversible Markov chain
• Infinite networks: I--Resistive networks
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