| Introduction 13 Function Space and Operator Theory for Nonlinear Analysis Introduction 1 Lp-Sobolev spaces 2 Sobolev imbedding theorems 3 Gagliardo-Nirenberg-Moser estimates 4 Tmdinger'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 References. 本书为英文版。 |
| Contents of Volumes I and II Introduction 13 Function Space and Operator Theory for Nonlinear Analysis Introduction 1 Lp-Sobolev spaces 2 Sobolev imbedding theorems 3 Gagliardo-Nirenberg-Moser estimates 4 Tmdinger‘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 References 14 Nonlinear Elliptic Equations Intxoduction 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-Ampere equations 16 Elliptic equations in two variables A Morrey spaces B Leray-Schauder fixed-point theorems References 15 Nonlinear Parabolic Equations Introduction 1 Semilinear 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 Introduction 1 Quasi-linear, symmetric hyperbolic systems 2 Symmetrizable hyperbolic systems 3 Second-order and higher-order hyperbolic 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 2×2 systems 10 Vibrating strings revisited Referen es 17 Euler and Navier-Stokes Equations for Incompressible Fluids 1 Introduction …… 18 Einstein's Equations Index |
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