變分法：理論與應(yīng)用

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