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Partial Differential Operators of Elliptic Type
 
Partial Differential Operators of Elliptic Type
Hardcover ISBN:  978-0-8218-4556-1
Product Code:  MMONO/99
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4511-9
Product Code:  MMONO/99.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4556-1
eBook: ISBN:  978-1-4704-4511-9
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
Partial Differential Operators of Elliptic Type
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Partial Differential Operators of Elliptic Type
Hardcover ISBN:  978-0-8218-4556-1
Product Code:  MMONO/99
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4511-9
Product Code:  MMONO/99.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4556-1
eBook ISBN:  978-1-4704-4511-9
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 Details
     
     
    Translations of Mathematical Monographs
    Volume: 991992; 288 pp
    MSC: 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, 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.

    Readership

    First 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. Vishik-Sobolev 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 first-year 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 991992; 288 pp
MSC: 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, 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.

Readership

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. Vishik-Sobolev 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 first-year 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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