经典数学丛书?偏微分方程 （第2版 影印版）（第3卷） 世界图书出版公司
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北京朝阳
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作者(美)泰勒 著
出版社世界图书出版公司
ISBN9787510068157
出版时间2014-01
装帧平装
开本24开
页数715页
定价109元
货号1200799672
上书时间2024-01-16
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内容简介
泰勒编著的这本《偏微分方程（第3卷第2版）》主要论述非线性偏微分方程。其中包括经典连续统力学方程和微分几何中的方程，以及非线性扩散问题。书中论及的分析方法包括索伯列夫空间理论、h-lder空间理论、hardy空间理论和morrey空间理论。本书目次如下：非线性分析用的泛函空间和算子理论；非线性椭圆方程；非线性抛物方程；非线性双曲方程；不可压缩流用的欧拉方程和navier-stokes方程；爱因斯坦方程。
本书读者对象：偏微分方程、数学物理、微分几何、调和分析和复分析等专业的研究生科研人员。
目录
Contents of Volumes I and H
Preface
13 Function Space and Operator Theory for Nonlinear Analysis
1 LP-Sobolev spaces
2 Sobolev imbedding theorems
3 Gagliardo-Nirenberg-Moser estimates
4 Trudinger's inequalities
5 Singular integral operators on Lp
6 The spaces Hs'p
7 LP-spectral theory of the Laplace operator
8 Holder spaces and Zygmund spaces
9 Pseudodifferential operators with nonregular symbols
10 Paradifferential operators
11 Young measures and fuzzy functions
12 Hardy spaces
A Variations on complex interpolation
References
14 Nonlinear Elliptic Equations
1 A class of semilinear equations
2 Surfaces with negative curvature
3 Local solvability of nonlinear elliptic equations
4 Elliptic regularity I (interior estimates)
5 Isometric imbedding of Riemannian manifolds
6 Minimal surfaces
6B Second variation of area
7 The minimal surface equation
8 Elliptic regularity II (boundary estimates)
9 Elliptic regularity III (DeGiorgi-Nash-Moser theory)
10 The Dirichlet problem for quasi-linear elliptic equations
11 Direct methods in the calculus of variations
12 Quasi-linear elliptic systems
12B Further results on quasi-linear systems
13 Elliptic regularity IV (Krylov-Safonov estimates)
14 Regularity for a class of completely nonlinear equations
15 Monge-Ampereequations
16 Elliptic equations in two variables
A Morrey spaces
B Leray-Schauder fixed-point theorems
References
15 Nonlinear Parabolic Equations
1 Semitinear parabolic equations
2 Applications to harmonic maps
3 Semilinear equations on regions with boundary
4 Reaction-diffusion equations
5 A nonlinear Trotter product formula
6 The Stefan problem
7 Quasi-linear parabolic equations I
8 Quasi-linear parabolic equations II (sharper estimates)
9 Quasi-linear parabolic equations III (Nash-Moser estimates)
References
16 Nonlinear Hyperbolic Equations
1 Quasi-linear， symmetric hyperbolic systems
2 Symmetrizable hyperbolic systems
3 Second-orderand higher-orderhyperbolic systems
4 Equations in the complex domain and the Cauchy- Kowalewsky theorem
5 Compressible fluid motion
6 Weak solutions to scalar conservation laws; the viscosity method
7 Systems of conservation laws in one space variable; Riemann problems
8 Entropy-flux pairs and Riemann invariants
9 Global weak solutions of some 2 x 2 systems
10 Vibrating strings revisited
References
17 Euler and Navier-Stokes Equations for Incompressible Fluids
1 Euler's equations for ideal incompressible fluid flow
2 Existence of solutions to the Euler equations
3 Euler flows on bounded regions
4 Navier-Stokes equations
5 VisCous flows on bounded regions
6 Vanishing viscosity limits
7 From velocity field convergence to flow convergence
A Regularity for the Stokes system on bounded domains
References
18 Einstein's Equations
1 The gravitational field equations
2 Spherically symmetric spacetimes and the Schwarzschild solution
3 Stationary and static spacetimes
4 Orbits in Schwarzschild spacetime
5 Coupled Maxwell-Einstein equations
6 Relativistic fluids
7 Gravitational collapse
8 The initial-value problem
9 Geometry of initial surfaces
10 Time slices and their evolution
References
Index
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