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Selected Chapters in the Calculus of Variations2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载
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- Jürgen Moser ; Oliver Knill 著
- 出版社: Birkhauser-Verlag
- ISBN:3764321857
- 出版时间:2003
- 标注页数:134页
- 文件大小:12MB
- 文件页数:143页
- 主题词:
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图书目录
0.1 Introduction1
0.2 On these lecture notes2
1 One-dimensional variational problems3
1.1 Regularity of the minimals3
1.2 Examples9
1.3 The accessory variational problem16
1.4 Extremal fields for n=120
1.5 The Hamiltonian formulation25
1.6 Exercises to Chapter 130
2 Extremal fields and global minimals33
2.1 Global extremal fields33
2.2 An existence theorem36
2.3 Properties of global minimals42
2.4 A priori estimates and a compactness property50
2.5 Mα for irrational α,Mather sets56
2.6 Mα for rational α73
2.7 Exercises to chapter Ⅱ81
3 Discrete Systems,Applications83
3.1 Monotone twist maps83
3.2 A discrete variational problem94
3.3 Three examples98
3.4 A second variational problem104
3.5 Minimal geodesics on T2105
3.6 Hedlund’s metric on T3108
3.7 Exercises to chapter Ⅲ113
Bibliography115
A Remarks on the literature117
Additional Bibliography121
Index129
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