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Analysis of Heat Equations on Domains. (LMS-31)
     

Analysis of Heat Equations on Domains. (LMS-31)

by El-Maati Ouhabaz
 

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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 Lp properties of solutions to a

Overview

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 Lp 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 Lp estimates for heat, Schrödinger, 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. The author supplies readers with several references for the few standard results that are stated without proofs.

Product Details

ISBN-13:
9781400826483
Publisher:
Princeton University Press
Publication date:
01/10/2009
Series:
London Mathematical Society Monographs
Sold by:
Barnes & Noble
Format:
NOOK Book
Pages:
296
File size:
27 MB
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What People are Saying About This

Alan McIntosh
This book is both an excellent introduction for those learning about heat operators for the first time, and a reference work for the mathematician searching for information. The author has presented an especially lucid exposition of the subject.
Alan McIntosh, Australian National University
Thierry Coulhon
This book contains very interesting material, starting with the basics and progressing to lively trends of current research.
Thierry Coulhon, Cergy-Pontoise University

Meet the Author

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

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