Introduction to heat potential theory
- Neil A. Watson.
- Providence, R.I. : American Mathematical Society, c2012.
- Physical description
- xiii, 266 p. ; 26 cm.
- Mathematical surveys and monographs ; no. 182.
Math & Statistics Library
QA3 .A4 V.182
- Unknown QA3 .A4 V.182
- Watson, N. A., 1948-
- Includes bibliographical references (p. 259-262) 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)
- Potential theory (Mathematics)
- Potential theory -- Research exposition (monographs, survey articles)
- Potential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions.
- Potential theory -- Higher-dimensional theory -- Potentials and capacities, extremal length.
- Potential theory -- Higher-dimensional theory -- Boundary value and inverse problems.
- Potential theory -- Higher-dimensional 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.
- Publication date
- Mathematical surveys and monographs ; v. 182
- 9780821849989 (alk. paper)
- 0821849980 (alk. paper)