[Résultats de stabilité pour les inégalités de Harnack]
Nous développons de nouvelles techniques pour obtenir des inégalités de Harnack uniformes elliptiques et paraboliques sur les variétés riemanniennes à poids. Nous démontrons en particulier la stabilité de ces inégalités pour certains changements de poids. Nous donnons une condition nécessaire et suffisante pour ces inégalités dans le cas des variétés riemanniennes complètes à courbure de Ricci positive ou nulle en dehors d'un compact et dont le premier nombre de Betti est fini, ou sous la condition de courbure sectionnelle asymptotiquement positive ou nulle.
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.
Keywords: Harnack inequality, Riemannian manifold, heat equation
Mot clés : inégalité de Harnack, variété riemannienne, équation de la chaleur
@article{AIF_2005__55_3_825_0,
author = {Grigor'yan, Alexander and Saloff-Coste, Laurent},
title = {Stability results for {Harnack} inequalities},
journal = {Annales de l'Institut Fourier},
pages = {825--890},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {55},
number = {3},
year = {2005},
doi = {10.5802/aif.2116},
mrnumber = {2149405},
zbl = {02171527},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2116/}
}
TY - JOUR AU - Grigor'yan, Alexander AU - Saloff-Coste, Laurent TI - Stability results for Harnack inequalities JO - Annales de l'Institut Fourier PY - 2005 SP - 825 EP - 890 VL - 55 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2116/ DO - 10.5802/aif.2116 LA - en ID - AIF_2005__55_3_825_0 ER -
%0 Journal Article %A Grigor'yan, Alexander %A Saloff-Coste, Laurent %T Stability results for Harnack inequalities %J Annales de l'Institut Fourier %D 2005 %P 825-890 %V 55 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2116/ %R 10.5802/aif.2116 %G en %F AIF_2005__55_3_825_0
Grigor'yan, Alexander; Saloff-Coste, Laurent. Stability results for Harnack inequalities. Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 825-890. doi : 10.5802/aif.2116. http://www.numdam.org/articles/10.5802/aif.2116/
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