A logarithmic Sobolev form of the Li-Yau parabolic inequality.

Bakry, Dominique, and Ledoux, Michel. "A logarithmic Sobolev form of the Li-Yau parabolic inequality.." Revista Matemática Iberoamericana 22.2 (2006): 683-702. <http://eudml.org/doc/41988>.

@article{Bakry2006,
abstract = {We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau parabolic inequality. This new inequality is of interest already in Euclidean space for the standard Gaussian measure. The result may also be seen as an extended version of the semigroup commutation properties under curvature conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev inequalities in this setting. Exponential Laplace differential inequalities through the Herbst argument furthermore yield diameter bounds and dimensional estimates on the heat kernel volume of balls.},
author = {Bakry, Dominique, Ledoux, Michel},
journal = {Revista Matemática Iberoamericana},
keywords = {Operadores diferenciales; Ecuación de difusión; Desigualdades de Sobolev; logarithmic Sobolev inequality; Li-Yau parabolic inequality; heat semigroup; gradient estimate; non-negative curvature; diameter bound},
language = {eng},
number = {2},
pages = {683-702},
title = {A logarithmic Sobolev form of the Li-Yau parabolic inequality.},
url = {http://eudml.org/doc/41988},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Bakry, Dominique
AU - Ledoux, Michel
TI - A logarithmic Sobolev form of the Li-Yau parabolic inequality.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 2
SP - 683
EP - 702
AB - We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau parabolic inequality. This new inequality is of interest already in Euclidean space for the standard Gaussian measure. The result may also be seen as an extended version of the semigroup commutation properties under curvature conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev inequalities in this setting. Exponential Laplace differential inequalities through the Herbst argument furthermore yield diameter bounds and dimensional estimates on the heat kernel volume of balls.
LA - eng
KW - Operadores diferenciales; Ecuación de difusión; Desigualdades de Sobolev; logarithmic Sobolev inequality; Li-Yau parabolic inequality; heat semigroup; gradient estimate; non-negative curvature; diameter bound
UR - http://eudml.org/doc/41988
ER -