A stability theorem for elliptic Harnack inequalities

Richard F. Bass

Journal of the European Mathematical Society (2013)

  • Volume: 015, Issue: 3, page 857-876
  • ISSN: 1435-9855

Abstract

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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.

How to cite

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Bass, Richard F.. "A stability theorem for elliptic Harnack inequalities." Journal of the European Mathematical Society 015.3 (2013): 857-876. <http://eudml.org/doc/277282>.

@article{Bass2013,
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.},
author = {Bass, Richard F.},
journal = {Journal of the European Mathematical Society},
keywords = {Harnack inequality; random walks on graphs; Poincaré inequality; cutoff inequality; metric measure space; Harnack inequality; random walks on graphs; Poincaré inequality; cutoff inequality; metric measure space},
language = {eng},
number = {3},
pages = {857-876},
publisher = {European Mathematical Society Publishing House},
title = {A stability theorem for elliptic Harnack inequalities},
url = {http://eudml.org/doc/277282},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Bass, Richard F.
TI - A stability theorem for elliptic Harnack inequalities
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 3
SP - 857
EP - 876
AB - 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.
LA - eng
KW - Harnack inequality; random walks on graphs; Poincaré inequality; cutoff inequality; metric measure space; Harnack inequality; random walks on graphs; Poincaré inequality; cutoff inequality; metric measure space
UR - http://eudml.org/doc/277282
ER -

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