Parabolic theory of the discrete \(p\)-Laplace operator

DOI10.1016/j.na.2013.04.002zbMath1285.39004arXiv1207.1996OpenAlexW1991844959MaRDI QIDQ393209

Delio Mugnolo

Publication date: 16 January 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.1996

zbMATH Keywords

porous medium equationdiscrete symmetriesdiscrete \(p\)-heat equationdiscrete \(p\)-Laplace operatordiscrete nonlinear diffusion-type problemfractional discrete differential equationnonlinear \(C_0\)-semigroups generated by subdifferentialsoperators on discrete graphs

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Heat equation (35K05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Discrete version of topics in analysis (39A12) Fractional partial differential equations (35R11) Quasilinear parabolic equations with (p)-Laplacian (35K92)

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Hemivariational inequalities on graphs ⋮ The generalized porous medium equation on graphs: existence and uniqueness of solutions with \(\ell^1\) data ⋮ General Cheeger inequalities for \(p\)-Laplacians on graphs ⋮ On quotients of spaces with Ricci curvature bounded below ⋮ On the orbital instability of excited states for the NLS equation with the \(\delta\)-interaction on a star graph ⋮ Dynamical systems associated with adjacency matrices ⋮ A non-local quasi-linear ground state representation and criticality theory ⋮ Existence and convergence of solutions for \(p\)-Laplacian systems with homogeneous nonlinearities on graphs ⋮ \(\psi\)-Li-Yau inequality for the \(p\)-Laplacian on weighted graphs with the \(CD_p^\psi (m, 0)\) curvature ⋮ Existence and multiplicity of solutions to \(p\)-Laplacian equations on graphs ⋮ The pth Kazdan–Warner equation on graphs ⋮ Edge connectivity and the spectral gap of combinatorial and quantum graphs ⋮ On the standing waves of the NLS-log equation with a point interaction on a star graph ⋮ EXISTENCE OF GLOBAL SOLUTIONS TO SOME NONLINEAR EQUATIONS ON LOCALLY FINITE GRAPHS ⋮ Time regularity and long-time behavior of parabolic \(p\)-Laplace equations on infinite graphs ⋮ Bi-Laplacians on graphs and networks ⋮ The Kazdan-Warner equation on canonically compactifiable graphs ⋮ Asymptotic estimates for the \(p\)-Laplacian on infinite graphs with decaying initial data ⋮ The 1-Yamabe equation on graphs

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