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Product Code:  MMONO/99 
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Product Code:  MMONO/99.E 
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Hardcover ISBN:  9780821845561 
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Hardcover ISBN:  9780821845561 
Product Code:  MMONO/99 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445119 
Product Code:  MMONO/99.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845561 
eBook ISBN:  9781470445119 
Product Code:  MMONO/99.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 99; 1992; 288 ppMSC: Primary 35
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, VishikSobolev 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.
ReadershipFirst year graduate students specializing in partial differential equations, researchers in other fields of mathematics.

Table of Contents

Chapters

Chapter I. Partial differential operators of elliptic type

Chapter II. The Laplacian in Euclidean spaces

Chapter III. Constructions and estimates of elementary solutions

Chapter IV. Smoothness of solutions

Chapter V. VishikSobolev problems

Chapter VI. General boundary value problems

Chapter VII. Schauder estimates and applications

Chapter VIII. Degenerate elliptic operators


Reviews

The book was designed for seniors or firstyear graduate students in Sendai specializing in elliptic partial differential equations, and will fill the same role admirably today in America or anywhere.
Mathematical Reviews 
Clear, well written, interesting; although it is addressed to (undergraduate or graduate) students, it is certainly useful for partial differential equations researchers as well.
Zentralblatt MATH


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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, VishikSobolev 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.
First year graduate students specializing in partial differential equations, researchers in other fields of mathematics.

Chapters

Chapter I. Partial differential operators of elliptic type

Chapter II. The Laplacian in Euclidean spaces

Chapter III. Constructions and estimates of elementary solutions

Chapter IV. Smoothness of solutions

Chapter V. VishikSobolev problems

Chapter VI. General boundary value problems

Chapter VII. Schauder estimates and applications

Chapter VIII. Degenerate elliptic operators

The book was designed for seniors or firstyear graduate students in Sendai specializing in elliptic partial differential equations, and will fill the same role admirably today in America or anywhere.
Mathematical Reviews 
Clear, well written, interesting; although it is addressed to (undergraduate or graduate) students, it is certainly useful for partial differential equations researchers as well.
Zentralblatt MATH