1977年，德国Springer出版了《二阶椭圆偏微分
方程》（Elliptic Partial Differential
Equations of Second Order, D. Gilbarg, S.
Trudinger）。20年之后的1996年，G. M. Lieberman
撰写了《二阶抛物微分方程》，成为《二阶椭圆偏微
分方程》的姊妹篇。几十年来，这两部书的均成为受
读者欢迎的经典教科书。
目录
PREFACE
PREFACE TO REVISED EDITION
Chapter Ⅰ INTRODUCTION
1.Outline of this book
2.Further remarks
3.Notation
Chapter Ⅱ MAXIMUM PRINCIPLES
Introduction
I.The weak maximum principle
2.The strong maximum principle
3.A priori estimates
Notes
Exercises
Chapter Ⅲ INTRODUCTION TO THE THEORY OF WEAK SOLUTIONS
Introduction
1.The theory of weak derivatives
2.The method of continuity
3.Problems in small balls
4.Global existence and the Perron process
Notes
Exercises
Chapter Ⅳ HOLDER ESTIMATES
Introduction
1.Ho1der continuity
2.Campanato spaces
3.Interior estimates
4.Estimates near a flat boundary
5.Regularized distance
6.Intermediate Schauder estimates
7.Curved boundaries and nonzero boundary data
8.Two special mixed problems
Notes
Exercises
Chapter Ⅴ EXISTENCE, UNIQUENESS AND REGULARITY OF SOLUTIONS
Introduction
1.Uniqueness of solutions
2.The Cauchy-Dirichlet problem with bounded coefficients
3.The Cauchy-Dirichlet problem with unbounded coefficients
4.The oblique derivative problem
Notes
Exercises
Chapter Ⅵ FURTHER THEORY OF WEAK SOLUTIONS
Introduction
1.Notation and basic results
2.Differentiability of weak solutions
3.Sobolev inequalities
4.Poincarf's inequality
5.Global boundedness
6.Local estimates
7.Consequences of the local estimates
