本書是一部經(jīng)典教材，初版于1977年，本版是1998年的重印版，書中對線性和擬線性二階橢圓型偏微分方程Dirichlet問題的理論進行了較詳細闡述。
目次：一、線性方程：Laplace方程；古典的最大值原理；Poisson方程和Newton勢；Banach空間和Hilbert空間；古典解和Schauder方法；Sobolev空間；廣義解和正則性；強解。二、擬線性方程：最大值原理和比較原理；拓撲不動點定理和應用；2個變量的方程；梯度的Holder估計；全局和內(nèi)梯度界；平均曲率型方程；完全非線性方程。
讀者對象：數(shù)學系高年級學生、研究生、教師和相關(guān)專業(yè)科學工作者。
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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