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变分法：理论及应用PDF|Epub|txt|kindle电子书版本下载
- 宣本金编著 著
- 出版社： 合肥：中国科学技术大学出版社
- ISBN：731201836X
- 出版时间：2006
- 标注页数：307页
- 文件大小：9MB
- 文件页数：319页
- 主题词：变分法－高等教育－教材－英文
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图书目录
1 Introduction1
1.1 Basic ideas of variational methods1
1.2 Classical solution and generalized solution4
Preface5
1.3 First variation,Euler-Lagrange equation6
1.4 Second variation14
1.5 Systems14
2 Sobolev Spaces21
2.1 H？lder spaces21
2.2 Lp spaces23
2.2.1 Useful inequalities25
2.2.2 Completeness of Lp(Ω)28
2.2.3 Dual space of Lp(Ω)29
2.2.4 Topologies in Lp(Ω)space31
2.2.5 Convolution36
2.2.6 Mollifier41
2.3 Sobolev spaces43
2.3.1 Weak derivatives43
2.3.2 Definition of Sobolev spaces45
2.3.3 Inequalities50
2.3.4 Embedding theorems and trace theorems55
3 Calculus in Banach Spaces63
3.1 Frechet-derivatives63
3.2 Nemyski operator67
3.3 Gateaux-derivatives70
3.4 Calculus of abstract functions74
3.5 Initial value problem in Banach space76
4 Direct Methods78
4.1 Lower semi-continuity78
4.2 A general lower semi-continuity result83
4.3 Ekeland variational principle87
4.4 Palais-Smale condition90
4.5 Constrained variational problems100
4.5.1 Lagrange multiplier method100
4.5.2 Weak sub-and super-solutions104
4.5.3 Nehari manifold107
5 Deformation Theorems112
5.1 Deformations in Hilbert space112
5.2 Pseudo-gradient vector field118
5.3 Deformations in Banach space122
6.1 General minimax principle135
6 Minimax Methods135
6.2 Mountain pass lemma139
6.3 Z2 index theory145
6.3.1 Minimax principles for even functionals148
6.3.2 Symmetric mountain pass lemma150
6.4 Linking argument157
6.5 p-Laplacian with indefinite weights162
6.5.1 Linking results163
6.5.2 Existence results165
7.1 Pohozaev type identities169
7 Noncompact Variational Problems169
7.2 Symmetry and compactness174
7.3 Concentration compactness principles181
7.3.1 The locally compact case181
7.3.2 The limit case191
7.4 Unconstrained problems involving critical Sobolev exponent197
7.4.1 Local compactness197
7.4.2 Nonhomogeneous problem208
7.4.3 Global compactness216
8.1 Solitary waves224
8 Generalized K-P Equation224
8.1.1 Existence of nontrivial solitary waves228
8.1.2 Nonexistence of nontrivial solitary waves231
8.2 Stationary solutions to GKP equation in bounded domain236
8.2.1 Existence results238
8.2.2 Nonexistence results240
9 Best Constants in Sobolev Inequalities245
9.1 Best constants245
9.1.1 l-dimensional case,Bliss Lemma246
9.1.2 m-dimensional case,symmetrization252
9.2.1 Yamabe problem254
9.2 Applications254
9.2.2 Problems with critical Sobolev exponents256
9.2.3 Global compactness259
9.3 Extensions260
9.3.1 Gagliardo-Nirenberg inequality260
9.3.2 The Caffarelli-Kohn-Nirenberg inequalities262
Appendix A Elliptic Regularity272
A.1 Local boundedness273
A.2 H？lder continuity283
Bibliography297
Index305