Partial differential operators of elliptic type
Author(s)
Bibliographic Information
Partial differential operators of elliptic type
（Translations of mathematical monographs, v. 99）
American Mathematical Society, c1992
- Other Title
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楕円形偏微分作用素
Daenkei henbibun sayōso
Available at 52 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
SHI||20||1(S)92026790
Note
Rev. translation of: 楕円形偏微分作用素 1978
Bibliographical references: p. 275-281
Includes index
Description and Table of Contents
Description
This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.
Table of Contents
Partial differential operators of elliptic type The Laplacian n Euclidean spaces Constructions and estimates of elementary solutions Smoothness of solutions Vishik-Sobolev problems General boundary value problems Schauder estimates and applications Degenerate elliptic operators.
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