Aspects of Sobolev-type inequalities / Laurent Saloff-Coste
Type de document : MonographieCollection : London Mathematical Society lecture note series, 289Langue : anglais.Pays: Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, 2002Description : 1 vol. (X-190 p.) ; 23 cmISBN: 0521006074.ISSN: 0076-0552.Bibliographie : Bibliogr. p. 183-188. Index.Sujet MSC : 46E35, Functional analysis - Linear function spaces and their duals, Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems46-02, Research exposition (monographs, survey articles) pertaining to functional analysis
35-02, Research exposition (monographs, survey articles) pertaining to partial differential equations
58J05, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Elliptic equations on manifolds, general theory
58J35, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Heat and other parabolic equation methodsEn-ligne : Zentralblatt | MathSciNet | CUP Item type:
Monographie
| Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|
| CMI Salle R | 46 SAL (Browse shelf(Opens below)) | Available | 01346-01 |
Bibliogr. p. 183-188. Index
This book focuses on Poincaré, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds. Applications covered include the ultracontractivity of the heat diffusion semigroup, Gaussian heat kernel bounds, the Rozenblum-Lieb-Cwikel inequality and elliptic and parabolic Harnack inequalities. Emphasis is placed on the role of families of local Poincaré and Sobolev inequalities. The text provides the first self contained account of the equivalence between the uniform parabolic Harnack inequality, on the one hand, and the conjunction of the doubling volume property and Poincaré's inequality on the other. (source : CUP)
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