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偏微分方程 第3卷 第2版 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （美）泰勒著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：9787510068157
- 出版时间：2014
- 标注页数：715页
- 文件大小：95MB
- 文件页数：733页
- 主题词：偏微分方程－研究生－教材－英文
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图书目录
13 Function Space and Operator Theory for Nonlinear Analysis1
1 Lp-Sobolev spaces2
2 Sobolev imbedding theorems4
3 Gagliardo-Nirenberg-Moser estimates8
4 Trudinger's inequalities14
5 Singular integral operators on Lp17
6 The spaces Hs,p24
7 Lp-spectral theory of the Laplace operator31
8 H？lder spaces and Zygmund spaces40
9 Pseudodifferential operators with nonregular symbols50
10 Paradifierential operators60
11 Young measures and fuzzy functions74
12 Hardy spaces86
A Variations on complex interpolation96
References102
14 Nonlinear Elliptic Equations105
1 A class of semilinear equations107
2 Surfaces with negative curvature119
3 Local solvability of nonlinear elliptic equations127
4 Elliptic regularity Ⅰ（interior estimates）135
5 Isometric imbedding of Riemannian manifolds147
6 Minimal surfaces152
6B Second variation of area168
7 The minimal surface equation176
8 Elliptic regularity Ⅱ（boundary estimates）185
9 Elliptic regularity Ⅲ（DeGiorgi-Nash-Moser theory）196
10 The Dirichlet problem for quasi-linear elliptic equations208
11 Direct methods in the calculus of variations222
12 Quasi-linear elliptic systems229
12B Further results on quasi-linear systems244
13 Elliptic regularity Ⅳ（Krylov--Safonov estimates）258
14 Regularity for a class of completely nonlinear equations273
15 Monge-Ampere equations282
16 Elliptic equations in two variables294
A Morrey spaces299
B Leray-Schauder fixed-point theorems302
References304
15 Nonlinear Parabolic Equations313
1 Semilinear parabolic equations314
2 Applications to harmonic maps325
3 Semilinear equations on regions with boundary332
4 Reaction-diffusion equations335
5 A nonlinear Trotter product formula353
6 The Stefan problem362
7 Quasi-linear parabolic equationsⅠ376
8 Quasi-linear parabolic equations Ⅱ（sharper estimates）387
9 Quasi-linear parabolic equations Ⅲ（Nash-Moser estimates）396
References407
16 Nonlinear Hyperbolic Equations413
1 Quasi-linear,symmetric hyperbolic systems414
2 Symmetrizable hyperbolic systems425
3 Second-order and higher-order hyperbolic systems432
4 Equations in the complex domain and the Cauchy-Kowalewsky theorem445
5 Compressible fluid motion448
6 Weak solutions to scalar conservation laws;the viscosity method457
7 Systems of conservation laws in one space variable;Riemann problems472
8 Entropy-flux pairs and Riemann invariants498
9 Global weak solutions of some 2×2 systems509
10 Vibrating strings revisited517
References524
17 Euler and Navier-Stokes Equations for Incompressible Fluids531
1 Euler's equations for ideal incompressible fluid flow532
2 Existence of solutions to the Euler equations542
3 Euler flows on bounded regions553
4 Navier-Stokes equations561
5 Viscous flows on bounded regions575
6 Vanishing viscosity limits586
7 From velocity field convergence to flow convergence599
A Regularity for the Stokes system on bounded domains605
References610
18 Einstein's Equations615
1 The gravitational field equations616
2 Spherically symmetric spacetimes and the Schwarzschild solution626
3 Stationary and static spacetimes639
4 Orbits in Schwarzschild spacetime649
5 Coupled Maxwell-Einstein equations656
6 Relativistic fluids659
7 Gravitational collapse670
8 The initial-value problem677
9 Geometry of initial surfaces687
10 Time slices and their evolution699
References705
Index711