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

Título inglés	A logarithmic Sobolev form of the Li-Yau parabolic inequality.
Título español	Una forma de Sobolev logarítmica de la desigualdad parabólica de Li-You.
Autor/es	Bakry, Dominique ; Ledoux, Michel
Organización	Inst. Math. Univ. Paul Sabatier, Toulouse, Francia
Revista	0213-2230
Publicación	2006, 22 (2): 683-702, 18 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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.
Clasificación UNESCO	120808
Palabras clave español	Operadores diferenciales ; Ecuación de difusión ; Desigualdades de Sobolev
Código MathReviews	MR2294794
Código Z-Math	Zbl pre05152587
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