A stability theorem for elliptic Harnack inequalities

A stability theorem for elliptic Harnack inequalities

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...

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Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2013-01, Vol.15 (3), p.857-876
1. Verfasser: Bass, Richard
Format: Artikel
Sprache:eng
Schlagworte:
Potential theory
Probability theory and stochastic processes
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Zusammenfassung: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.
ISSN:1435-9855
1435-9863
DOI:10.4171/JEMS/379