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Liouville properties on graphs

Part of: Other generalizations

Published online by Cambridge University Press:  26 February 2010

Marco Rigoli ,
Maura Salvatori  and
Marco Vignati
Marco Rigoli
Affiliation:
Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italy.
Maura Salvatori
Affiliation:
Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italy.
Marco Vignati
Affiliation:
Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italy.
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Abstract

We introduce a class of “differential operators” on graphs and we prove an energy estimate and a Liouville type theorem depending on some structural properties of the operators considered.

MSC classification

Secondary: 31C05: Harmonic, subharmonic, superharmonic functions
Type
Research Article
Information
Mathematika , Volume 44 , Issue 1 , June 1997 , pp. 133 - 148
Copyright
Copyright © University College London 1997

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References

DK.Dodziuk, J. and Karp, L.. Spectral and function theory for combinatorial Laplacians. Contemporary Mathematics, 73 (1988), 25–40.CrossRefGoogle Scholar
H.Hwang, J. F.. Comparison principles and Liouville theorems for prescribed mean curvature equations in unbounded domains. Ann. Scuola Norm. Sup. Pisa, 15 (1988), 341–355.Google Scholar
N.-WNash-Williams, C. St. J. A.. Random walks and electric currents in networks. Proc. Cambridge Phil. Soc., 55 (1959), 181–194.CrossRefGoogle Scholar
RSV.Rigoli, M., Salvatori, M. and Vignati, M.. Subharmonic functions on graphs. Israel J. Math. To appear.Google Scholar
S.Soardi, P. M.. Potential Theory in Infinite Networks, Lecture Notes in Math., 1590 (Springer Verlag, 1994).CrossRefGoogle Scholar
W.Woess, W.. Random walks on infinite graphs and groups—a survey on selected topics. Bull. London Math. Soc., 26 (1994), 1–60.CrossRefGoogle Scholar