This book provides a self-contained development of the regularity theory for solutions of fully nonlinear elliptic equations. Caffarelli and Cabre offer a detailed presentation of all techniques needed to extend the classical Schauder and Calderon-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.

This book provides a self-contained development of the regularity theory for solutions of fully nonlinear elliptic equations. Caffarelli and Cabre offer a detailed presentation of all techniques needed to extend the classical Schauder and Calderon-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.