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

Delmotte, T.

Colloq. Math. 72, No. 1, 19-37 (1997).

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

Keywords:

Harnack inequality; Moser’s iteration; strongly local Dirichlet forms

Citations:

Zbl 0760.49004; Zbl 0854.35016