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Introduction to Heat Potential Theory (Mathematical Surveys and Monographs) 🔍
American Mathematical Society, Mathematical Surveys and Monographs, Mathematical Surveys and Monographs 182, 2012
Neil A. Watson 🔍
description
This book is the first to be devoted entirely to the potential theory of the heat equation, and thus deals with time dependent potential theory. Its purpose is to give a logical, mathematically precise introduction to a subject where previously many proofs were not written in detail, due to their similarity with those of the potential theory of Laplace's equation. The approach to subtemperatures is a recent one, based on the Poisson integral representation of temperatures on a circular cylinder. Characterizations of subtemperatures in terms of heat balls and modified heat balls are proved, and thermal capacity is studied in detail. The generalized Dirichlet problem on arbitrary open sets is given a treatment that reflects its distinctive nature for an equation of parabolic type. Also included is some new material on caloric measure for arbitrary open sets. Each chapter concludes with bibliographical notes and open questions. The reader should have a good background in the calculus of functions of several variables, in the limiting processes and inequalities of analysis, in measure theory, and in general topology for Chapter 9.
Alternative filename
lgrsnf/75/M_Mathematics/MC_Calculus/MCf_Functional analysis/Watson N.A. Introduction to heat potential theory (SURV182, AMS, 2012)(ISBN 9780821849989)(O)(282s)_MCf_.pdf
Alternative filename
lgli/75/M_Mathematics/MC_Calculus/MCf_Functional analysis/Watson N.A. Introduction to heat potential theory (SURV182, AMS, 2012)(ISBN 9780821849989)(O)(282s)_MCf_.pdf
Alternative filename
lgli/M_Mathematics/MC_Calculus/MCf_Functional analysis/Watson N.A. Introduction to heat potential theory (SURV182, AMS, 2012)(ISBN 9780821849989)(O)(282s)_MCf_.pdf
Alternative filename
nexusstc/Introduction to Heat Potential Theory/5e14e33215468be4cad13b271daebbb0.pdf
Alternative author
Watson, Neil A
Alternative edition
Mathematical surveys and monographs -- vol. 182, Providence, R. I, United States, 2012
Alternative edition
Mathematical surveys and monographs -- v. 182, Providence, R.I, Rhode Island, 2012
Alternative edition
Mathematical surveys and monographs (Online), Providence (R.I.), 2012
Alternative edition
American Mathematical Society, Providence, Rhode Island, 2012
Alternative edition
United States, United States of America
metadata comments
kolxoz -- 75
metadata comments
lg1415315
metadata comments
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metadata comments
Includes bibliographical references and index.
metadata comments
Указ.
Библиогр.: с. 259-262
metadata comments
РГБ
metadata comments
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Alternative description
This Book Is The First To Be Devoted Entirely To The Potential Theory Of The Heat Equation, And Thus Deals With Time Dependent Potential Theory. ... The Generalized Dirichlet Problem On Arbitrary Open Sets Is Given A Treatment That Reflects Its Distinctive Nature For An Equation Of Parabolic Type. Also Included Is Some New Material On Caloric Measure For Arbitrary Open Sets.--publisher's Description. The Heat Operator, Temperatures And Mean Values -- The Poisson Integral For A Circular Cylinder -- Subtemperatures And The Dirichlet Problem On Convex Domains Of Revolution -- Temperatures On An Infinite Strip -- Classes Of Subtemperatures On An Infinite Strip -- Green Functions And Heat Potentials -- Polar Sets And Thermal Capacity -- The Dirichlet Problem On Arbitrary Open Sets -- The Thermal Fine Topology. Neil A. Watson. Includes Bibliographical References (p. 259-262) And Index.
Alternative description
Cover 1
Title page 2
Contents 4
Preface 8
Notation and terminology 12
The heat operator, temperatures and mean values 16
The Poisson integral for a circular cylinder 50
Subtemperatures and the Dirichlet problem on convex domains of revolution 68
Temperatures on an infinite strip 100
Classes of subtemperatures on an infinite strip 120
Green functions and heat potentials 142
Polar sets and thermal capacity 174
The Dirichlet problem on arbitrary open sets 210
The thermal fine topology 246
Bibliography 274
Index 278
Back Cover 282
Alternative description
This is the first book to be devoted entirely to the potential theory of the heat equation, and thus deals with time dependent potential theory. Its purpose is to give a logical, mathematically precise introduction to a subject where previously many proofs were not written in detail, due to their similarity with those of the potential theory of Laplace's equation.
date open sourced
2015-12-12
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