**Colloquium Publications**

Volume: 43;
1995;
104 pp;
Softcover

MSC: Primary 35;

Print ISBN: 978-0-8218-0437-7

Product Code: COLL/43

List Price: $38.00

Individual Member Price: $30.40

**Electronic ISBN: 978-1-4704-3189-1
Product Code: COLL/43.E**

List Price: $38.00

Individual Member Price: $30.40

# Fully Nonlinear Elliptic Equations

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*Luis A. Caffarelli; Xavier Cabré*

This book provides a self-contained 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 Calderón-Zygmund 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.

#### Table of Contents

# Table of Contents

## Fully Nonlinear Elliptic Equations

- Cover Cover11
- Title page iii4
- Contents v6
- Introduction 18
- Chapter 1. Preliminaries 512
- Chapter 2. Viscosity solutions of elliptic equations 1118
- Chapter 3. Alexandroff estimate and maximum principle 2128
- Chapter 4. Harnack inequality 2936
- Chapter 5. Uniqueness of solutions 4350
- Chapter 6. Concave equations 5158
- Chapter 7. 𝑊^{2,𝑝} Regularity 5966
- Chapter 8. Hölder regularity 7380
- Chapter 9. The Dirichlet problem for concave equations 8592
- Bibliography 99106
- Index 103110
- Back Cover Back Cover1113

#### Readership

Researchers and graduate students interested in elliptic partial differential 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