Fully Nonlinear Elliptic Equations (Colloquium Publications (Amer Mathematical Soc))

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. <P>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.

"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