本书是一部经典教材，初版于1977年，本版是1998年的重印版，书中对线性和拟线性二阶椭圆型偏微分方程Dirichlet问题的理论进行了较详细阐述。
目次：一、线性方程：Laplace方程；古典的最大值原理；Poisson方程和Newton势；Banach空间和Hilbert空间；古典解和Schauder方法；Sobolev空间；广义解和正则性；强解。二、拟线性方程：最大值原理和比较原理；拓扑不动点定理和应用；2个变量的方程；梯度的Holder估计；全局和内梯度界；平均曲率型方程；完全非线性方程。
读者对象：数学系高年级学生、研究生、教师和相关专业科学工作者。
Chapter 1. Introduction
Part Ⅰ Linear Equations
Chapter 2 Laplace’s Equation
2.1 The Mean Value Inequalities
2.2 Maximum and Minimum Principle
2.3 The Harnack Inequality
2.4 Green’s Representation
2.5 The Poisson Integral
2.6 Convergence Theorems
2.7 Interior Estimates of Derivatives
2.8 The Dirichlet Problem； the Method of Subharmonic Functions
2.9 Capacity
Problems
Chapter 3 The Classical Maximum Principle
3.1 The Weak Maximum Principle
3.2 The Strong Maximum Principle
3.3 Apriori Bounds
3.4 Gradient Estimates for Poisson’s Equation
3.5 A Harnack Inequality
3.6 Operators in Divergence Form
Notes
Problems
Chapter 4 Poissons Equation and the Newtonian Potential
4.1 Holder Continuity
4.2 The Dirichlet Problem for Poissons Equation
4.3 Holder Estimates for the Second Derivatives
4.4 Eximates at the Boundary
4.5 Holder Estimates for the First Derivatives
Notes
Problems
Chapter 5 Banach and Hilbert Spaces
5.1 The Contraction Mapping Principle
5.2 The Method of Continity
5.3 The Fredholm Alternative
5.4 Dual Spaces and Adjoints
5.5 Hilbert Spaces
5.6 The Projection Theorem
5.7 The Riesz Represenation Theorem
5.8 The Lax-Milgram Theorem
5.9 The Fredholm Alternative in Hilbert Spaces
5.10 Weak Compactness
Notes
Problems
Chapter 6 Calssical Solutions; the Schauder Approach
Chapter 7 Sobolev Spaces
Chapter 8 Generalized Solutiona and regularity
Chapter 9 Strong Solutions
Part Ⅱ Quasilinear Equations
Chapter 10 Maximum and Comparison Principles
Chapter 11 Topological Fixed Point Theorems and Their Application
Chapter 12 Equation in Two Varables
Chapter 13 Holder Extimates for the Cradient
Chapter 14 Boundary Gradient Estimates
Chapter 15 Global and Interior Gradient Bounds
Chapter 16 Equations of Mean Curvature Type
Chapter 17 Fully Nonlinear Equations
Bibliography
Epilogue
Subject Index
Notation Index
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