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
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