Analysis of Heat Equations on Domains

El Maati Ouhabaz - Collection Mathematics/Physics

284 pages, parution le 30/11/2004

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Résumé

This is the first comprehensive reference published on heat equations associated with non-self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats L^p properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory, and mathematical physics.

This book addresses new developments and applications of Gaussian upper bounds to spectral theory. In particular, it shows how such bounds can be used in order to prove L^p estimates for heat, Schrodinger, and wave type equations. A significant part of the results have been proved during the last decade.

The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second-order elliptic operators in divergence form, heat kernel bounds, and their applications. It will also be of value to mathematical physicists.

L'auteur - El Maati Ouhabaz

El Maati Ouhabaz is Professor of Analysis and Geometry at Universite Bordeaux 1.

Sommaire

Preface
Notation
Sesquilinear forms, associated operators, and Semigroups
Contractivity properties
Inequalities for sub-markovian semigroups
Uniformly elliptic operators on domains
Degenerate-elliptic operators
Gaussian upper bounds for heat kernels
Gaussian upper bounds and zaspectral theory
A review of the kato square root problem
Bibliography
Index

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	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	El Maati Ouhabaz
Collection	Mathematics/Physics
Parution	30/11/2004
Nb. de pages	284
Format	16 x 24
Couverture	Relié
Poids	536g
Intérieur	Noir et Blanc
EAN13	9780691120164
ISBN13	978-0-691-12016-4