A logarithmic Sobolev form of the Li-Yau parabolic inequality | Zendy

Dominique Bakry | Zendy; Michel Ledoux | Zendy

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A logarithmic Sobolev form of the Li-Yau parabolic inequality

Author(s) -

Dominique Bakry,

Michel Ledoux

Publication year - 2006

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/470

Subject(s) - mathematics , heat kernel , sobolev inequality , logarithm , mathematical analysis , euclidean space , semigroup , curvature , pure mathematics , sobolev space , geometry

We present a finite dimensional version of the logarith- mic Sobolev inequality for heat kernel measures of non-negatively curved diusion 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 curva- ture conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev inequalities in this setting. Exponential Laplace dierential in-

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