Stability of parabolic Harnack inequalities

Barlow, Martin; Bass, Richard

doi:10.1090/S0002-9947-03-03414-7

Stability of parabolic Harnack inequalities
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by Martin T. Barlow and Richard F. Bass PDF

Trans. Amer. Math. Soc. 356 (2004), 1501-1533 Request permission

Abstract:

Let $(G,E)$ be a graph with weights $\{a_{xy}\}$ for which a parabolic Harnack inequality holds with space-time scaling exponent $\beta \ge 2$. Suppose $\{a’_{xy}\}$ is another set of weights that are comparable to $\{a_{xy}\}$. We prove that this parabolic Harnack inequality also holds for $(G,E)$ with the weights $\{a’_{xy}\}$. We also give stable necessary and sufficient conditions for this parabolic Harnack inequality to hold.

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