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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.Read more
- This is the first book covering the recent advances in Harnack inequalities on manifolds
- Provides a detailed treatment of Sobolev inequalities on Riemannian manifolds
- Suitable as a textbook for advanced graduate courses
Reviews & endorsements
'The book is very well written and organized. it contains so many comments and explanations that both experts and non-experts on the subject may enjoy reading it.' Zentralblatt für MathematikSee more reviews
'… a well-written and self-contained account of the topic.' EMS Newsletter
'[This book] constitues a valuable addition to the modern theory of inequalities.' Bulletin of the Belgian Mathematical Society
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- Date Published: December 2001
- format: Paperback
- isbn: 9780521006071
- length: 202 pages
- dimensions: 228 x 153 x 14 mm
- weight: 0.286kg
- availability: Available
Table of Contents
1. Sobolev inequalities in Rn
2. Moser's elliptic Harnack Inequality
3. Sobolev inequalities on manifolds
4. Two applications
5. Parabolic Harnack inequalities.
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