
Preface  Preview Material  Table of Contents  Index  Supplementary Material 
Mathematical Surveys and Monographs 2012; 266 pp; hardcover Volume: 182 ISBN10: 0821849980 ISBN13: 9780821849989 List Price: US$86 Member Price: US$68.80 Order Code: SURV/182 See also: The Ricci Flow: Techniques and Applications: Part III: GeometricAnalytic Aspects  Bennett Chow, SunChin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo and Lei Ni Second Order Equations of Elliptic and Parabolic Type  E M Landis  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. Readership Graduate students and research mathematicians interested in partial differential equations and potential theory. 


AMS Home 
Comments: webmaster@ams.org © Copyright 2014, American Mathematical Society Privacy Statement 