Sobolev spaces on locally finite graphs

Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs on graphs and networks (ramified or polygonal spaces) (35R02) Sobolev (and similar kinds of) spaces of functions of discrete variables (46E39) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

General Cheeger inequalities for $p$-Laplacians on graphs
Parabolic theory of the discrete $p$-Laplace operator
Kazdan-Warner equation on graph
Stochastic completeness for graphs with curvature dimension conditions
Yamabe type equations on graphs
Functional analysis, Sobolev spaces and partial differential equations
A nodal domain theorem and a higher-order Cheeger inequality for the graph $p$-Laplacian
Existence of positive solutions to some nonlinear equations on locally finite graphs
A discrete Schrödinger equation via optimal transport on graphs
Convergence of ground state solutions for nonlinear Schrödinger equations on graphs
Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs
$p$-Laplacian equations on locally finite graphs
Normalized discrete Ricci flow used in community detection
The existence of extremal functions for discrete Sobolev inequalities on lattice graphs
Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs
Existence and convergence of solutions for nonlinear biharmonic equations on graphs
Dirichlet $p$-Laplacian eigenvalues and Cheeger constants on symmetric graphs
Discrete approximations of metric measure spaces of controlled geometry
Semigroup methods for evolution equations on networks
Sur un théorème d'analyse fonctionnelle.
Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales.
Calculus of variations on locally finite graphs
Sobolev spaces on graphs
On the $p$-Laplacian and $\infty$-Laplacian on Graphs with Applications in Image and Data Processing
Spectrum of the 1-Laplacian and Cheeger's Constant on Graphs
Eigenvalues of Graphs and Sobolev Inequalities
Graphs and Discrete Dirichlet Spaces
Nonlocal PDEs-Based Morphology on Weighted Graphs for Image and Data Processing

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