《偏微分方程（第2版）》是一套3卷集经典名著，第一版曾影印出版，广受好评。第2版新增内容312页（3卷），这是第2卷。泰勒编著的这本《偏微分方程（第2卷第2版）》在第1卷的基础上进一步讨论线性偏微分方程中的一些高等问题，其中包括伪微分算子、自伴算子的泛函分析和wiener测度。书中还介绍了微分几何的基本概念、椭圆微分算子的谱理论、由障碍产生的波动散射理论、狄拉克算子用的指数理论、布朗运动和扩散等。本书目次如下：伪微分算子；谱论；由障碍产生的散射；狄拉克算子和指数理论；布朗运动和位势论；-neumann问题；联络和曲率。

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 III

Preface

7 Pseudodifferential Operators

 1 The Fourier integral representation and symbol classes

 2 Schwartz kernels of pseudodifferential operators

 3 Adjoints and products

 4 Elliptic operators and parametrices

 5 L2-estimates

 6 Gading's inequality

 7 Hyperbolic evolution equations

 8 Egorov's theorem

 9 Microlocal regularity

 10 Operators on manifolds

 11 The method of layer potentials

 12 Parametrix for regular elliptic boundary problems

 13 Parametrix for the heat equation

 14 The Weyl calculus

 15 Operators of harmonic oscillator type

 References

8 Spectral Theory

 1 The spectral theorem

 2 Self-adjoint differential operators

 3 Heat asymptotics and eigenvalue asymptotics

 4 The Laplace operator on Sn

 5 The Laplace operator on hyperbolic space

 6 The harmonic oscillator

 7 The quantum Coulomb problem

 8 The Laplace operator on cones

 References

9 Scattering by Obstacles

 1 The scattering problem

 2 Eigenfunction expansions

 3 The scattering operator

 4 Connections with the wave equation

 5 Wave operators

 6 Translation representations and the Lax-Phillips semigroup Z(t)

 7 Integral equations and scattering poles

 8 Trace formulas; the scattering phase

 9 Scattering by a sphere

 10 Inverse problems I

 11 Inverse problems lI

 12 Scattering by rough obstacles

 A Lidskii's trace theorem

 References

10 Dirae Operators and Index Theory

 1 Operators of Dirac type

 2 Clifford algebras

 3 Spinors

 4 Weitzenbock formulas

 5 Index of Dirac operators

 6 Proof of the local index formula

 7 The Chern-Gauss-Bonnet theorem

 8 Spinc manifolds

 9 The Riemann-Roch theorem

 10 Direct attack in 2-D

 11 Index of operators of harmonic oscillator type

 References

11 Brownian Motion and Potential Theory

 1 Brownian motion and Wiener measure

 2 The Feynman-Kac formula

 3 The Dirichlet problem and diffusion on domains with boundary

 4 Martingales, stopping times, and the strong Markov property

 5 First exit time and the Poisson integral

 6 Newtonian capacity

 7 Stochastic integrals

 8 Stochastic integrals, II

 9 Stochastic differential equations

 10 Application to equations of diffusion

 A The Trotter product formula

 References

12 The a-Neumann Problem

 A Elliptic complexes

 1 The O-complex

 2 Morrey's inequality, the Levi form, and strong pseudoconvexity

 3 The 1-estimate and some consequences

 4 Higher-order subelliptic estimates

 5 Regularity via elliptic regularization

 6 The Hodge decomposition and the 0-equation

 7 The Bergman projection and Toeplitz operators

 8 The a-Neumann problem on (O, q)-forms

 9 Reduction to pseudodifferential equations on the boundary

 10 The J-equation on complex manifolds and almost complex manifolds

 B Complements on the Levi form

 C The Neumann operator for the Dirichlet problem

 References

C Connections and Curvature

 1 Covariant derivatives and curvature on general vector bundles

 2 Second covariant derivatives and covariant-exterior derivatives

 3 The curvature tensor of a Riemannian manifold

 4 Geometry of submanifolds and subbundles

 5 The Gauss-Bonnet theorem for surfaces

 6 The principal bundle picture

 7 The Chern-Weil construction

 8 The Chern--Gauss-Bonnet theorem

 References

Index