# A stability theorem for elliptic Harnack inequalities

### Richard F. Bass

University of Connecticut, Storrs, United States

## Abstract

We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for harmonic functions with respect to the other graph. As part of the proof, we give a characterization of the elliptic Harnack inequality.

## Cite this article

Richard F. Bass, A stability theorem for elliptic Harnack inequalities. J. Eur. Math. Soc. 15 (2013), no. 3, pp. 857–876

DOI 10.4171/JEMS/379