路易斯·卡法雷利、泽维尔·卡雷著的《完全非线性椭圆方程(英文版)(精)》系统介绍了完全非线性椭圆方程解的正则理论的最新进展。作者详细描述了将线性椭圆方程的经典Schauder和CaIderon-Zygmund正则理论推广到完全非线性情形的所有技巧。
作者介绍了完全非线性方程粘性解的正则理论的主要思想，并证明了所有结果。书中还包括对凸完全非线性方程和具有变系数的完全非线性方程的研究内容。

Introduction
1.Preliminaries
1.1.Basic Notation and Terminology
1.2.Tangent Paraboloids and Second Order Differentiability
2.Viscosity Solutions of Elliptic Equations
2.1.Viscosity Solutions
2.2.The Class S of Solutions of Uniformly Elliptic Equations
2.3.Examples of Fully Nonlinear Elliptic Equations
Notes
3.Alexandroff Estimate and Maximum Principle
3.1.Alexandroff-Bakelman—Pucci Estimate
Notes
4.Harnack Inequality
4.1.Two Important Tools
4.2.Harnack Inequalitv
4.3.CαRegularity
5.Uniqueness of Solutions
5.1.Jensen's Approximate Solutions
5.2.Uniqueness for F(D2u)=0
5.3.C1，αRegularity for F(D2u)=0
5.4.Applications to Concave Equations
Notes
6.Concave Equations
6.1.Evans-Krylov Theorem
6.2.C2，αRegularity for F(D2u)=0
7.W2，pRegularity
7.1.W2，p Estimates
8.H61der Regularity
8.1.C2，α Estimates
8.2.Cl，αEstimates
9.The Dirichlet Problem for Concave Equations
9.1.Bernstein's Technique
9.2.C2，α Estimate up to the Boundary for F(D2u)=0
9.3.The Dirichlet Problem
Bibliography
Index