Harmonic functions of general graph Laplacians
We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an L p Liouville type theorem which is a quantitative integral L p estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s L p -L...
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Veröffentlicht in: | Calculus of variations and partial differential equations 2014-09, Vol.51 (1-2), p.343-362 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
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Zusammenfassung: | We study harmonic functions on general weighted graphs which allow for a compatible intrinsic metric. We prove an
L
p
Liouville type theorem which is a quantitative integral
L
p
estimate of harmonic functions analogous to Karp’s theorem for Riemannian manifolds. As corollaries we obtain Yau’s
L
p
-Liouville type theorem on graphs, identify the domain of the generator of the semigroup on
L
p
and get a criterion for recurrence. As a side product, we show an analogue of Yau’s
L
p
Caccioppoli inequality. Furthermore, we derive various Liouville type results for harmonic functions on graphs and harmonic maps from graphs into Hadamard spaces. |
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ISSN: | 0944-2669 1432-0835 |
DOI: | 10.1007/s00526-013-0677-6 |