Aspects of Sobolev-Type Inequalities (London Mathematical Society Lecture Note Series) by Laurent Saloff-Coste

Aspects of Sobolev-Type Inequalities (London Mathematical Society Lecture Note Series)



Download Aspects of Sobolev-Type Inequalities (London Mathematical Society Lecture Note Series)




Aspects of Sobolev-Type Inequalities (London Mathematical Society Lecture Note Series) Laurent Saloff-Coste
Language: English
Page: 202
Format: pdf
ISBN: 0521006074, 9780521006071
Publisher: Cambridge University Press

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.

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