Geodesic
A stability theorem for elliptic Harnack inequalities
Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 857-876

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/379
Classification : 31-XX, 60-XX, 00-XX
Keywords: Harnack inequality, random walks on graphs, Poincaré inequality, cutoff inequality, metric measure space 
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     author = {Richard F. Bass},
     title = {A stability theorem for elliptic {Harnack} inequalities},
     journal = {Journal of the European Mathematical Society},
     pages = {857--876},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2013},
     doi = {10.4171/jems/379},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/379/}
}
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Richard F. Bass. A stability theorem for elliptic Harnack inequalities. Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 857-876. doi: 10.4171/jems/379

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