Aspects of Sobolev-Type Inequalities
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Aspects of Sobolev-Type Inequalities: (Series Number 289 London Mathematical Society Lecture Note Series)

Aspects of Sobolev-Type Inequalities: (Series Number 289 London Mathematical Society Lecture Note Series)


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About the Book

This book, first published in 2001, 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. 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.

Table of Contents:
Preface; Introduction; 1. Sobolev inequalities in Rn; 2. Moser's elliptic Harnack Inequality; 3. Sobolev inequalities on manifolds; 4. Two applications; 5. Parabolic Harnack inequalities.

Review :
'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 Mathematik '… 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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Product Details
  • ISBN-13: 9780511549762
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press (Virtual Publishing)
  • Language: English
  • ISBN-10: 0511549768
  • Publisher Date: 06 Aug 2010
  • Binding: Digital download and online
  • Series Title: Series Number 289 London Mathematical Society Lecture Note Series


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Aspects of Sobolev-Type Inequalities: (Series Number 289 London Mathematical Society Lecture Note Series)
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Aspects of Sobolev-Type Inequalities: (Series Number 289 London Mathematical Society Lecture Note Series)
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