Introduction to heat potential theory
 Author/Creator
 Watson, N. A., 1948
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xiii, 266 p. ; 26 cm.
 Series
 Mathematical surveys and monographs ; no. 182.
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Available online

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QA3 .A4 V.182

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QA3 .A4 V.182
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 259262) and index.
 Publisher's Summary
 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Potential theory (Mathematics)
 Potential theory  Research exposition (monographs, survey articles)
 Potential theory  Higherdimensional theory  Harmonic, subharmonic, superharmonic functions.
 Potential theory  Higherdimensional theory  Potentials and capacities, extremal length.
 Potential theory  Higherdimensional theory  Boundary value and inverse problems.
 Potential theory  Higherdimensional theory  Boundary behavior.
 Potential theory  Other generalizations  Harmonic, subharmonic, superharmonic functions.
 Potential theory  Other generalizations  Potentials and capacities.
 Partial differential equations  Research exposition (monographs, survey articles)
 Partial differential equations  Parabolic equations and systems  Heat equation.
Bibliographic information
 Publication date
 2012
 Responsibility
 Neil A. Watson.
 Series
 Mathematical surveys and monographs ; v. 182
 ISBN
 9780821849989 (alk. paper)
 0821849980 (alk. paper)