偏微分方程(第3卷)(第2版)

出版时间：2013-1-1  作者：Michael E. Taylor  

书籍目录

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