Aspects of Sobolev-Type Inequalities

This book focuses on Poincar , 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 Poincar 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 Poincar 's inequality on the other.

Author: Laurent Saloff-Coste
Publisher: Cambridge University Press
Published: 11/22/2001
Pages: 202
Binding Type: Paperback
Weight: 0.61lbs
Size: 8.93h x 6.10w x 0.40d
ISBN: 9780521006071