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Fully Nonlinear Elliptic Equations
Luis A. Caffarelli and Xavier Cabré, Institute for Advanced Study, Princeton, NJ
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Colloquium Publications
1995; 104 pp; softcover
Volume: 43
Reprint/Revision History:
reprinted 1997
ISBN-10: 0-8218-0437-5
ISBN-13: 978-0-8218-0437-7
List Price: US$36
Member Price: US$28.80
Order Code: COLL/43
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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.

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

Table of Contents

  • Introduction
  • Preliminaries
  • Viscosity solutions of elliptic equations
  • Alexandroff estimate and maximum principle
  • Harnack inequality
  • Uniqueness of solutions
  • Concave equations
  • \(W^{2,p}\) regularity
  • Hölder regularity
  • The Dirichlet problem for concave equations
  • Bibliography
  • Index
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