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