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Elliptic Harnack inequality on graphs. (Inégalité de Harnack elliptique sur les graphes.) (French) Zbl 0871.31008

The author proves an Harnack inequality for an elliptic operator on an infinite connected locally uniformly finite graph by Moser’s iteration. It would be interesting to make a comparison with the results obtained in the general framework of strongly local Dirichlet forms used in the paper of M. Biroli and U. Mosco [C. R. Acad. Sci., Paris, Sér. I 313, No. 9, 593-598 (1991; Zbl 0760.49004)] extended by K. T. Sturm to the parabolic case [J. Math. Pures Appl., IX. Sér. 75, No. 3, 273-297 (1996; Zbl 0854.35016)] (those papers do not appear in the references).
Reviewer: M.Biroli (Monza)

MSC:

31C25 Dirichlet forms
35B45 A priori estimates in context of PDEs
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