Softcover ISBN:  9780821804377 
Product Code:  COLL/43 
List Price:  $41.00 
MAA Member Price:  $36.90 
AMS Member Price:  $32.80 
Electronic ISBN:  9781470431891 
Product Code:  COLL/43.E 
List Price:  $38.00 
MAA Member Price:  $34.20 
AMS Member Price:  $30.40 

Book DetailsColloquium PublicationsVolume: 43; 1995; 104 ppMSC: Primary 35;
This book provides a selfcontained development of the regularity theory for solutions of fully nonlinear elliptic equations. Caffarelli and Cabré offer a detailed presentation of all techniques needed to extend the classical Schauder and CalderónZygmund regularity theories for linear elliptic equations to the fully nonlinear context.
The authors present the key ideas and prove all the results needed for the regularity theory of viscosity solutions of fully nonlinear equations. The book contains the study of convex fully nonlinear equations and fully nonlinear equations with variable coefficients.
This book is suitable as a text for graduate courses in nonlinear elliptic partial differential equations.ReadershipResearchers and graduate students interested in elliptic partial differential equations.

Table of Contents

Chapters

Introduction

Chapter 1. Preliminaries

Chapter 2. Viscosity solutions of elliptic equations

Chapter 3. Alexandroff estimate and maximum principle

Chapter 4. Harnack inequality

Chapter 5. Uniqueness of solutions

Chapter 6. Concave equations

Chapter 7. $W^{2,p}$ Regularity

Chapter 8. Hölder regularity

Chapter 9. The Dirichlet problem for concave equations


Reviews

The book marks an important stage in the theory of nonlinear elliptic problems. Its timely appearance will surely stimulate fresh attacks on the many difficult and interesting questions which remain.
Bulletin of the LMS 
Interesting and well written … contains material selected with good taste … likely to be highly appreciated both by researchers and advanced students.
Mathematical Reviews 
Well written, with the arguments clearly presented. There are helpful remarks throughout the book, and at several points the authors give the main ideas of the more technical proofs before proceeding to the details … will certainly be of interest to researchers and graduate students in the field of nonlinear elliptic equations.
Bulletin of the AMS


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This book provides a selfcontained development of the regularity theory for solutions of fully nonlinear elliptic equations. Caffarelli and Cabré offer a detailed presentation of all techniques needed to extend the classical Schauder and CalderónZygmund regularity theories for linear elliptic equations to the fully nonlinear context.
The authors present the key ideas and prove all the results needed for the regularity theory of viscosity solutions of fully nonlinear equations. The book contains the study of convex fully nonlinear equations and fully nonlinear equations with variable coefficients.
This book is suitable as a text for graduate courses in nonlinear elliptic partial differential equations.
Researchers and graduate students interested in elliptic partial differential equations.

Chapters

Introduction

Chapter 1. Preliminaries

Chapter 2. Viscosity solutions of elliptic equations

Chapter 3. Alexandroff estimate and maximum principle

Chapter 4. Harnack inequality

Chapter 5. Uniqueness of solutions

Chapter 6. Concave equations

Chapter 7. $W^{2,p}$ Regularity

Chapter 8. Hölder regularity

Chapter 9. The Dirichlet problem for concave equations

The book marks an important stage in the theory of nonlinear elliptic problems. Its timely appearance will surely stimulate fresh attacks on the many difficult and interesting questions which remain.
Bulletin of the LMS 
Interesting and well written … contains material selected with good taste … likely to be highly appreciated both by researchers and advanced students.
Mathematical Reviews 
Well written, with the arguments clearly presented. There are helpful remarks throughout the book, and at several points the authors give the main ideas of the more technical proofs before proceeding to the details … will certainly be of interest to researchers and graduate students in the field of nonlinear elliptic equations.
Bulletin of the AMS