Analysis of heat equations on domains / El Maati Ouhabaz.

Format:

Book

Author/Creator:

Ouhabaz, El Maati.

Series:

London Mathematical Society Monographs

London mathematical society monograph series ; v. 31

Language:

English

Subjects (All):

Heat equation.

Heat--Transmission--Measurement.

Heat.

Physical Description:

1 online resource (298 p.)

Edition:

Course Book

Place of Publication:

Princeton, N.J. : Princeton University Press, c2005.

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Contents

Preface

Notation

Chapter One. Sesquilinear Forms, Associated Operators, and Semigroups

Chapter Two. Contractivity Properties

Chapter Three. Inequalities for Sub-Markovian Semigroups

Chapter Four. Uniformly Elliptic Operators on Domains

Chapter Five. Degenerate-Elliptic Operators

Chapter Six. Gaussian Upper Bounds for Heat Kernels

Chapter Seven. Gaussian Upper Bounds and Lp-Spectral Theory

Chapter Eight. A Review of the Kato Square Root Problem

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [265]-282) and index.

ISBN:

9786612157387

9781282157385

1282157388

9781400826483

1400826489

OCLC:

436943847