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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
Available Formats:
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 Electronic 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
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List Price: $52.50 MAA Member Price:$47.25
AMS Member Price: $42.00 Click above image for expanded view 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 Available Formats:  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
 Electronic 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 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$52.50 MAA Member Price: $47.25 AMS Member Price:$42.00
• 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.

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
• 2.5. 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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
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.

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
• 2.5. 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 reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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