Aspects of Sobolev-Type Inequalities
By (author) Laurent Saloff-Coste
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Aspects of Sobolev-Type Inequalities by Laurent Saloff-Coste
Book DescriptionThis book, first published in 2001, focuses on Poincare, 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 Poincare 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 Poincare's inequality on the other. It is suitable to be used as an advanced graduate textbook and will also be a useful source of information for graduate students and researchers in analysis on manifolds, geometric differential equations, Brownian motion and diffusion on manifolds, as well as other related areas.
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Book DetailsISBN: 9780521006071
(228mm x 152mm x 12mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 22-Nov-2001
Country of Publication: United Kingdom
Books By Author Laurent Saloff-Coste
Analysis and Geometry on Groups, Paperback (December 2008)» View all books by Laurent Saloff-Coste
The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups.
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