Stability results for Harnack inequalities

Alexander Grigor'yan[1]; Laurent Saloff-Coste

  • [1] Imperial college, department of mathematics, London SW7 2BZ (United kingdom), Cornell University, department of mathematics, Malott Hall, Ithaca NY 14853-4201 (USA)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 3, page 825-890
  • ISSN: 0373-0956

Abstract

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We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically non-negative sectional curvature.

How to cite

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Grigor'yan, Alexander, and Saloff-Coste, Laurent. "Stability results for Harnack inequalities." Annales de l’institut Fourier 55.3 (2005): 825-890. <http://eudml.org/doc/116210>.

@article{Grigoryan2005,
abstract = {We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically non-negative sectional curvature.},
affiliation = {Imperial college, department of mathematics, London SW7 2BZ (United kingdom), Cornell University, department of mathematics, Malott Hall, Ithaca NY 14853-4201 (USA)},
author = {Grigor'yan, Alexander, Saloff-Coste, Laurent},
journal = {Annales de l’institut Fourier},
keywords = {Harnack inequality; Riemannian manifold; heat equation},
language = {eng},
number = {3},
pages = {825-890},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stability results for Harnack inequalities},
url = {http://eudml.org/doc/116210},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Grigor'yan, Alexander
AU - Saloff-Coste, Laurent
TI - Stability results for Harnack inequalities
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 3
SP - 825
EP - 890
AB - We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically non-negative sectional curvature.
LA - eng
KW - Harnack inequality; Riemannian manifold; heat equation
UR - http://eudml.org/doc/116210
ER -

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