《偏微分方程（第3卷·第2 版）》是2013年世界圖書出版公司出版的著作，作者是Michael E. Taylor。
基本介紹
- 書名：《偏微分方程（第3卷·第2 版）》
- 作者：Michael E. Taylor
- 出版社：世界圖書出版公司
- 出版時間：2013-1-1
內容提要,目錄,
內容提要
本書這是一套3卷*經典名著，*版曾*出版，廣受好評。2版新增內容312頁（3卷），這是3卷。本卷主要論述*線性偏微分方程。其中*括經典連續統力學方程和微分幾何中的方程，以及*線性擴散問題。書中論及的分析方法*括索伯列夫空間理論、hlder空間理論、hardy空間理論和morrey空間理論。*線性分析用的泛函空間和運算元理論；*線性橢圓方程；*線性拋物方程；*線性雙曲方程；不可壓縮流用的歐拉方程和navier-stokes方程；愛因斯坦方程。讀者對象：偏微分方程、數學物理、微分幾何、調和分析和複分析等專*的研究生科研人員。
讀者對象：偏微分方程、數學物理、微分幾何、調和分析和複分析等專*的研究生科研人員。
讀者對象：偏微分方程、數學物理、微分幾何、調和分析和複分析等專*的研究生科研人員。
目錄
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
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
