Hardcover ISBN:  9781470426071 
Product Code:  GSM/171 
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eBook ISBN:  9781470429065 
Product Code:  GSM/171.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470426071 
eBook: ISBN:  9781470429065 
Product Code:  GSM/171.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Hardcover ISBN:  9781470426071 
Product Code:  GSM/171 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470429065 
Product Code:  GSM/171.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470426071 
eBook ISBN:  9781470429065 
Product Code:  GSM/171.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 171; 2016; 368 ppMSC: Primary 35
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler–Einstein metrics.
This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge–Ampère equations. It gives a userfriendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing selfcontained, clear, and “elementary” proofs for results in important special cases. This book will serve as a valuable resource for graduate students or anyone interested in this subject.
ReadershipGraduate students and research mathematicians interested in nonlinear PDE and applications to differential geometry.

Table of Contents

Chapters

Introduction

Chapter 1. Linear elliptic equations

Part 1. Quasilinear elliptic equations

Chapter 2. Quasilinear uniformly elliptic equations

Chapter 3. Mean curvature equations

Chapter 4. Minimal surface equations

Part 2. Fully nonlinear elliptic equations

Chapter 5. Fully nonlinear uniformly elliptic equations

Chapter 6. MongeAmpère equations

Chapter 7. Complex MongeAmpère equations

Chapter 8. Generalized solutions of MongeAmpère equations


Additional Material

Reviews

[T]he book of Han will serve as a valuable resource for graduate students and for anyone interested in the subject of nonlinear second order elliptic PDEs.
Dian K. Palagachev, Zentralblatt MATH


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Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler–Einstein metrics.
This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge–Ampère equations. It gives a userfriendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing selfcontained, clear, and “elementary” proofs for results in important special cases. This book will serve as a valuable resource for graduate students or anyone interested in this subject.
Graduate students and research mathematicians interested in nonlinear PDE and applications to differential geometry.

Chapters

Introduction

Chapter 1. Linear elliptic equations

Part 1. Quasilinear elliptic equations

Chapter 2. Quasilinear uniformly elliptic equations

Chapter 3. Mean curvature equations

Chapter 4. Minimal surface equations

Part 2. Fully nonlinear elliptic equations

Chapter 5. Fully nonlinear uniformly elliptic equations

Chapter 6. MongeAmpère equations

Chapter 7. Complex MongeAmpère equations

Chapter 8. Generalized solutions of MongeAmpère equations

[T]he book of Han will serve as a valuable resource for graduate students and for anyone interested in the subject of nonlinear second order elliptic PDEs.
Dian K. Palagachev, Zentralblatt MATH