变分法-理论与应用

本书不仅对变分法的基本概念、理论和方法作了严谨的介绍和论述，而且特别注重介绍变为法在解决椭圆型方程中的应用等内容。

Preface
1 Introduction
1.1 Basic ideas of variatinal methods
1.2 Classical solution and generalized solution
1.3 First variation,Euler-Lagrange equation
1.4 Second variation
1.5 Systems
2 Sobolev Spaces
2.1 Holder spaces
2.2 Lp spaces
2.2.1 Useful inequalities
2.2.2 Completeness of Lp（Ω）
2.2.3 Dual space of Lp（Ω）
2.2.4 Topologies in Lp（Ω）space
2.2.5 Convolution
2.2.6 Mollifier
2.3 Sobolev spaces
2.3.1 Weak derivatives
2.3.2 Definition of Sobolev spaces
2.3.3 Inequalities
2.3.4 Embedding theorems and trace theorems
3 Calulus in Banach Spaces
3.1 Frechet-derivatives
3.2 Nemyski poerator
3.3 Gateaux-derivatives
3.4 Calculus of abstract functions
3.5 Initial value problem in Banach space
4 Direct Methods
5 Deformation Theorems
6 Minimax Methods
7 Noncompact Variational Problems
8 Generalized K-P Equation
9 Best Constants in Sobolev Inequalities
Appendix A Elliptic Regularity
Bibliography
Index