Aspects of Sobolev-Type Inequalities

by Laurent Saloff-Coste

Overview

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.

Product Details

ISBN-13:	9780521006071
Publisher:	Cambridge University Press
Publication date:	11/22/2001
Series:	London Mathematical Society Lecture Note Series , #289
Pages:	202
Product dimensions:	6.02(w) x 8.98(h) x 0.55(d)

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.

Editorial Reviews

'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

From the Publisher