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
[