Delmotte, T. Elliptic Harnack inequality on graphs. (Inégalité de Harnack elliptique sur les graphes.) (French) Zbl 0871.31008 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) Cited in 18 Documents 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 PDF BibTeX XML Cite \textit{T. Delmotte}, Colloq. Math. 72, No. 1, 19--37 (1997; Zbl 0871.31008) Full Text: DOI EuDML OpenURL