Parabolic theory of the discrete p-Laplace operator

Abstract

We study the discrete version of the $p$-Laplacian. Based on its variational properties we discuss some features of the associated parabolic problem. Our approach allows us in turn to obtain interesting information about positivity and comparison principles as well as compatibility with the symmetries of the graph. We conclude briefly discussing the variational properties of a handful of nonlinear generalized Laplacians appearing in different parabolic equations.

35 pages several corrections and enhancements in comparison to the v1

References in corpus (5)

• Tug-of-war and the infinity Laplacian
• Lack of Sphere Packing of Graphs via Non-Linear Potential Theory
• Well-Posedness and Symmetries of Strongly Coupled Network Equations
• The L2 strong maximum principle on arbitrary countable networks
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Cited by in corpus (7)

• Time regularity and long-time behavior of parabolic $p$-Laplace equations on infinite graphs
• Edge connectivity and the spectral gap of combinatorial and quantum graphs
• On quotients of spaces with Ricci curvature bounded below
• Bi-Laplacians on graphs and networks
• General Cheeger inequalities for p-Laplacians on graphs
• Dynamical systems associated with adjacency matrices
• The Kazdan-Warner equation on canonically compactifiable graphs