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。

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