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    • 作者: (美)泰勒著
    • 出版社: 世界图书出版公司
    • 出版时间:2014-01-01 00:00:00
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    商品参数
    • 作者: (美)泰勒著
    • 出版社:世界图书出版公司
    • 出版时间:2014-01-01 00:00:00
    • 版次:1
    • 印次:1
    • 印刷时间:2014-01-01
    • 页数:715
    • 开本:24开
    • 装帧:平装
    • ISBN:9787510068157
    • 国别/地区:中国
    • 版权提供:世界图书出版公司

    偏微分方程

    作  者:(美)泰勒 著
    定  价:109
    出 版 社:世界图书出版公司
    出版日期:2014年01月01日
    页  数:715
    装  帧:平装
    ISBN:9787510068157
    主编推荐

    内容简介

    泰勒编著的这本《偏微分方程(第3卷第2版)》主要论述非线性偏微分方程。其中包括经典连续统力学方程和微分几何中的方程,以及非线性扩散问题。书中论及的分析方法包括索伯列夫空间理论、h-lder空间理论、hardy空间理论和morrey空间理论。本书目次如下:非线性分析用的泛函空间和算子理论;非线性椭圆方程;非线性抛物方程;非线性双曲方程;不可压缩流用的欧拉方程和navier-stokes方程;爱因斯坦方程。
    本书读者对象:偏微分方程、数学物理、微分几何、调和分析和复分析等专业的研究生科研人员。

    作者简介

    精彩内容

    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

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