Aspects of Sobolev-Type Inequalities

Aspects of Sobolev-Type Inequalities

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Description

This 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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 1139237403
  • 9781139237406

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.show more

Review quote

'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 fur 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 Societyshow more