We prove a global Harnack inequality for positive p-harmonic functions on a graph Gamma provided a weak Poincare inequality holds on Gamma and the counting measure of Gamma is doubling. Consequently, every positive p-harmonic function on such a graph must be constant

Holopainen, I., Soardi, P. (1997). A strong Liouville theorem for p-harmonic functions on graphs. ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA, 22(1), 205-226.

A strong Liouville theorem for p-harmonic functions on graphs

SOARDI, PAOLO MAURIZIO
1997

Abstract

We prove a global Harnack inequality for positive p-harmonic functions on a graph Gamma provided a weak Poincare inequality holds on Gamma and the counting measure of Gamma is doubling. Consequently, every positive p-harmonic function on such a graph must be constant
Articolo in rivista - Articolo scientifico
$p$-harmonic functions on graphs; $p$-Laplacian; Harnack inequality; Liouville theorem
English
1997
22
1
205
226
none
Holopainen, I., Soardi, P. (1997). A strong Liouville theorem for p-harmonic functions on graphs. ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA, 22(1), 205-226.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/18361
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