Several characterizations of p-parabolicity (Ahlfors, Kelvin-Nevanlinna-Royden, Khas'minskiĭ, Poincaré) hold on infinite locally summable graphs for p-energy functionals, with applications to the p-Laplacian obstacle problem via finite-graph approximation.
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Characterizations of $p$-Parabolicity on Graphs
Several characterizations of p-parabolicity (Ahlfors, Kelvin-Nevanlinna-Royden, Khas'minskiĭ, Poincaré) hold on infinite locally summable graphs for p-energy functionals, with applications to the p-Laplacian obstacle problem via finite-graph approximation.