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偏微分方程 第2卷 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （德）索维尼著 著
- 出版社： 世界图书出版公司北京公司
- ISBN：7510035173
- 出版时间：2011
- 标注页数：392页
- 文件大小：13MB
- 文件页数：405页
- 主题词：
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图书目录
Ⅶ Operators in Banach Spaces1
1 Fixed point theorems1
2 The Leray-Schauder degree of mapping12
3 Fundamental properties for the degree of mapping18
4 Linear operators in Banach spaces22
5 Some historical notices to the chapters Ⅲ and Ⅶ29
Ⅷ Linear Operators in Hilbert Spaces31
1 Various eigenvalue problems31
2 Singular integral equations45
3 The abstract Hilbert space54
4 Bounded linear operators in Hilbert spaces64
5 Unitary operators75
6 Completely continuous operators in Hilbert spaces87
7 Spectral theory for completely continuous Hermitian operators103
8 The Sturm-Liouville eigenvalue problem110
9 Weyl's eigenvalue problem for the Laplace operator117
9 Some historical notices to chapter Ⅷ125
Ⅸ Linear Elliptic Differential Equations127
1 The differential equation ⊿φ＋p（x,y）φx＋q（x,y）φy＝r（x,y）127
2 The Schwarzian integral formula133
3 The Riemann-Hilbert boundary value problem136
4 Potential-theoretic estimates144
5 Schauder's continuity method156
6 Existence and regularity theorems161
7 The Schauder estimates169
8 Some historical notices to chapter Ⅸ185
Ⅹ Weak Solutions of Elliptic Differential Equations187
1 Sobolev spaces187
2 Embedding and compactness201
3 Existence of weak solutions208
4 Boundedness of weak solutions213
5 H？lder continuity of weak solutions216
6 Weak potential-theoretic estimates227
7 Boundary behavior of weak solutions234
8 Equations in divergence form239
9 Green's function for elliptic operators245
10 Spectral theory of the Laplace-Beltrami operator254
11 Some historical notices to chapter Ⅹ256
Ⅺ Nonlinear Partial Differential Equations259
1 The fundamental forms and curvatures of a surface259
2 Two-dimensional parametric integrals265
3 Quasilinear hyperbolic differential equations and systems of second order （Characteristic parameters）274
4 Cauchy's initial value problem for quasilinear hyperbolic differential equations and systems of second order281
5 Riemann's integration method291
6 Bernstein's analyticity theorem296
7 Some historical notices to chapter Ⅺ302
Ⅻ Nonlinear Elliptic Systems305
1 Maximum principles for the H-surface system305
2 Gradient estimates for nonlinear elliptic systems312
3 Global estimates for nonlinear systems324
4 The Dirichlet problem for nonlinear elliptic systems328
5 Distortion estimates for plane elliptic systems336
6 A curvature estimate for minimal surfaces344
7 Global estimates for conformal mappings with respect to Riemannian metrics348
8 Introduction of conformal parameters into a Riemannian metric357
9 The uniformization method for quasilinear elliptic differential equations and the Dirichlet problem362
10 An outlook on Plateau's problem374
11 Some historical notices to chapter Ⅻ379
References383
Index385