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Introduction to Heat Potential Theory

Neil A. Watson University of Canterbury, Christchurch, New Zealand
Available Formats:
Hardcover ISBN: 978-0-8218-4998-9
Product Code: SURV/182
266 pp
List Price: $92.00 MAA Member Price:$82.80
AMS Member Price: $73.60 Electronic ISBN: 978-0-8218-8792-9 Product Code: SURV/182.E 266 pp List Price:$86.00
MAA Member Price: $77.40 AMS Member Price:$68.80
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List Price: $138.00 MAA Member Price:$124.20
AMS Member Price: $110.40 Click above image for expanded view Introduction to Heat Potential Theory Neil A. Watson University of Canterbury, Christchurch, New Zealand Available Formats:  Hardcover ISBN: 978-0-8218-4998-9 Product Code: SURV/182 266 pp  List Price:$92.00 MAA Member Price: $82.80 AMS Member Price:$73.60
 Electronic ISBN: 978-0-8218-8792-9 Product Code: SURV/182.E 266 pp
 List Price: $86.00 MAA Member Price:$77.40 AMS Member Price: $68.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$138.00
MAA Member Price: $124.20 AMS Member Price:$110.40
• Book Details

Mathematical Surveys and Monographs
Volume: 1822012
MSC: Primary 31; 35;

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.

Graduate students and research mathematicians interested in partial differential equations and potential theory.

• Chapters
• 1. The heat operator, temperatures and mean values
• 2. The Poisson integral for a circular cylinder
• 3. Subtemperatures and the Dirichlet problem on convex domains of revolution
• 4. Temperatures on an infinite strip
• 5. Classes of subtemperatures on an infinite strip
• 6. Green functions and heat potentials
• 7. Polar sets and thermal capacity
• 8. The Dirichlet problem on arbitrary open sets
• 9. The thermal fine topology

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Volume: 1822012
MSC: Primary 31; 35;

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.

Graduate students and research mathematicians interested in partial differential equations and potential theory.

• Chapters
• 1. The heat operator, temperatures and mean values
• 2. The Poisson integral for a circular cylinder
• 3. Subtemperatures and the Dirichlet problem on convex domains of revolution
• 4. Temperatures on an infinite strip
• 5. Classes of subtemperatures on an infinite strip
• 6. Green functions and heat potentials
• 7. Polar sets and thermal capacity
• 8. The Dirichlet problem on arbitrary open sets
• 9. The thermal fine topology
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