Aspects of Sobolev-Type Inequalities

This book, first published in 2001, is a concise introduction to analysis on manifolds, covering functional inequalities and their applications, for graduates and researchers.

Laurent Saloff-Coste (Author)

9780521006071, Cambridge University Press

Paperback, published 22 November 2001

202 pages
22.8 x 15.3 x 1.4 cm, 0.286 kg

'[This book] constitues a valuable addition to the modern theory of inequalities.' Bulletin of the Belgian Mathematical Society

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.

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.

Subject Areas: Geometry [PBM], Calculus & mathematical analysis [PBK]