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Elliptic Partial Differential Equations: Second Edition
 
Qing Han University of Notre Dame, Notre Dame, IN
Fanghua Lin Courant Institute, New York University, New York, NY
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Elliptic Partial Differential Equations
Softcover ISBN:  978-0-8218-5313-9
Product Code:  CLN/1.R
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
eBook ISBN:  978-1-4704-1136-7
Product Code:  CLN/1.R.E
List Price: $33.00
MAA Member Price: $29.70
AMS Member Price: $26.40
Softcover ISBN:  978-0-8218-5313-9
eBook: ISBN:  978-1-4704-1136-7
Product Code:  CLN/1.R.B
List Price: $68.00 $51.50
MAA Member Price: $61.20 $46.35
AMS Member Price: $54.40 $41.20
Elliptic Partial Differential Equations
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Elliptic Partial Differential Equations: Second Edition
Qing Han University of Notre Dame, Notre Dame, IN
Fanghua Lin Courant Institute, New York University, New York, NY
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Softcover ISBN:  978-0-8218-5313-9
Product Code:  CLN/1.R
List Price: $35.00
MAA Member Price: $31.50
AMS Member Price: $28.00
eBook ISBN:  978-1-4704-1136-7
Product Code:  CLN/1.R.E
List Price: $33.00
MAA Member Price: $29.70
AMS Member Price: $26.40
Softcover ISBN:  978-0-8218-5313-9
eBook ISBN:  978-1-4704-1136-7
Product Code:  CLN/1.R.B
List Price: $68.00 $51.50
MAA Member Price: $61.20 $46.35
AMS Member Price: $54.40 $41.20
  • Book Details
     
     
    Courant Lecture Notes
    Volume: 12011; 147 pp
    MSC: Primary 35;

    Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things about it—it is a wonderful book.

    Tobias Colding

    This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.

    This second edition has been thoroughly revised and in a new chapter the authors discuss several methods for proving the existence of solutions of primarily the Dirichlet problem for various types of elliptic equations.

    Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

    Readership

    Graduate students and research mathematicians interested in elliptic PDEs.

  • Table of Contents
     
     
    • Front Cover
    • Contents
    • Preface
    • CHAPTER 1: Harmonic Functions
    • 1.1. Guide
    • 1.2. Mean Value Properties
    • 1.3. Fundamental Solutions
    • 1.4. Maximum Principles
    • 1.5. Energy Method
    • CHAPTER 2Maximum Principles
    • 2.1. Guide
    • 2.2. Strong Maximum Principle
    • 2.3. A Priori Estimates
    • 2.4. Gradient Estimates
    • 2.5. Alexandroff Maximum Principle
    • 2.6. Moving Plane Method
    • CHAPTER 3: Weak Solutions: Part I
    • 3.1. Guide
    • 3.2. Growth of Local Integrals
    • 3.3. Hölder Continuity of Solutions
    • 3.4. Hölder Continuity of Gradients
    • CHAPTER 4: Weak Solutions, Part II
    • 4.1. Guide
    • 4.2. Local Boundedness
    • 4.3. Hölder Continuity
    • 4.4. Moser’s Harnack Inequality
    • 4.5. Nonlinear Equations
    • CHAPTER 5: Viscosity Solutions
    • 5.1. Guide
    • 5.2. Alexandroff Maximum Principle
    • 5.3. Harnack Inequality
    • 5.4. Schauder Estimates
    • 5.5. W 2;p Estimates
    • 5.6. Global Estimates
    • CHAPTER 6: Existence of Solutions
    • 6.1. Perron Method
    • 6.2. Variational Method
    • 6.3. Continuity Method
    • 6.4. Compactness Methods
    • 6.5. Single- and Double-Layer Potentials Methods
    • 6.6. Fixed-Point Theorems and Existence Results
    • Bibliography
    • Titles in This Series
    • Back Cover
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 12011; 147 pp
MSC: Primary 35;

Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things about it—it is a wonderful book.

Tobias Colding

This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.

This second edition has been thoroughly revised and in a new chapter the authors discuss several methods for proving the existence of solutions of primarily the Dirichlet problem for various types of elliptic equations.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Readership

Graduate students and research mathematicians interested in elliptic PDEs.

  • Front Cover
  • Contents
  • Preface
  • CHAPTER 1: Harmonic Functions
  • 1.1. Guide
  • 1.2. Mean Value Properties
  • 1.3. Fundamental Solutions
  • 1.4. Maximum Principles
  • 1.5. Energy Method
  • CHAPTER 2Maximum Principles
  • 2.1. Guide
  • 2.2. Strong Maximum Principle
  • 2.3. A Priori Estimates
  • 2.4. Gradient Estimates
  • 2.5. Alexandroff Maximum Principle
  • 2.6. Moving Plane Method
  • CHAPTER 3: Weak Solutions: Part I
  • 3.1. Guide
  • 3.2. Growth of Local Integrals
  • 3.3. Hölder Continuity of Solutions
  • 3.4. Hölder Continuity of Gradients
  • CHAPTER 4: Weak Solutions, Part II
  • 4.1. Guide
  • 4.2. Local Boundedness
  • 4.3. Hölder Continuity
  • 4.4. Moser’s Harnack Inequality
  • 4.5. Nonlinear Equations
  • CHAPTER 5: Viscosity Solutions
  • 5.1. Guide
  • 5.2. Alexandroff Maximum Principle
  • 5.3. Harnack Inequality
  • 5.4. Schauder Estimates
  • 5.5. W 2;p Estimates
  • 5.6. Global Estimates
  • CHAPTER 6: Existence of Solutions
  • 6.1. Perron Method
  • 6.2. Variational Method
  • 6.3. Continuity Method
  • 6.4. Compactness Methods
  • 6.5. Single- and Double-Layer Potentials Methods
  • 6.6. Fixed-Point Theorems and Existence Results
  • Bibliography
  • Titles in This Series
  • Back Cover
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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