# [PDF] Aspects of Sobolev-Type Inequalities (London Mathematical Society Lecture Note Series)

#### ISBN: 0521006074

#### Category: Tutorial

Posted on 2017-10-09, by luongquocchinh.

Description

Author: Laurent Saloff-Coste | Publisher: Cambridge University Press | Category: Medicine | Language: English | Page: 202 | ISBN: 0521006074 | ISBN13: 9780521006071 |

**Description:**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.

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