Aspects of Sobolev-Type Inequalities

ISBN-13: 9780521006071 / Angielski / Miękka / 2001 / 202 str.

Laurent Saloff-Coste; Laurent Salofof-Coste; L. Saloff-Coste

Opis

This book 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.

Recenzje

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

Spis treści

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.