Sur les inégalités de Sobolev logarithmiques / Cécile Ané, Sébastien Blachère, Djalil Chafai, ... [et al.] ; avec une préface de Dominique Bakry et Michel Ledoux

Auteur principal : Ané, Cécile, AuteurCo-auteur : Blachère, Sébastien, Auteur • Chafaï, Djalil, AuteurAuteur secondaire : Ledoux, Michel, 1958-, Préfacier • Bakry, Dominique, 1954-, PréfacierType de document : MonographieCollection : Panoramas et synthèses, 10Langue : français.Pays: France.Éditeur : Paris : Société Mathématique de France, 2000Description : 1 vol. (217 p.) : fig. ; 24 cmISBN: 9782856291054.ISSN: 1272-3835.Bibliographie : Bibliogr. p. 197-213. Index.Sujet MSC : 46E35, Functional analysis - Linear function spaces and their duals, Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems
60J60, Probability theory and stochastic processes - Markov processes, Diffusion processes
58J65, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Diffusion processes and stochastic analysis on manifolds
94A17, Communication, information, Measures of information, entropy
47D07, Operator theory - Groups and semigroups of linear operators, their generalizations and applications, Markov semigroups and applications to diffusion processes
En-ligne : Sommaire
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The book is a pedestrian approach to logarithmic Sobolev inequalities, accessible to a wide audience. It is divided into chapters of independent interest. The fundamental example of two Bernoulli and Gaussian distributions is the starting point to logarithmic Sobolev inequalities as they were defined by Gross in the mid-seventies. Hypercontractivity and tensorisation form two main aspects of these inequalities, that are actually part of the larger family of classical Sobolev inequalities in functional analysis. (Zentralblatt)

Bibliogr. p. 197-213. Index

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