偏微分方程（第3卷）

出版时间：1999-6  出版社：世界图书出版公司  作者：M.E.Taylor  页数：608  
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内容概要

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

书籍目录

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　References15 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)　References16 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 es17 Euler and Navier-Stokes Equations for Incompressible Fluids　1 Introduction  ……18 Einstein's EquationsIndex