《偏微分方程(第2卷)》是一部两卷集的偏微分方程教材。多变量椭圆，抛物和双曲方程是研究的主要对象，解决了pde和多变量方法之间的关系。本书是第二卷主要讲述了banach空间算子方程的可解性，hilbert空间线性算子和谱理论；线性椭圆微分方程的schauder理论；微分方程弱解；非线性偏微分方程；非线性椭圆系统和微分几何应用。书中各章的独立性较强，有一定偏微分方程基本知识的读者可以独立阅读各章。本书由索维尼等著。

7 Operators in Banach Spaces

Fixed point theorems

The Leray-Schauder degree of mapping

Fundamental properties for the degree of mapping

Linear operators in Banach spaces

Some historical notices to the chapters III and VII

8 Linear Operators in Hilbert Spaces

Various eigenvalue problems

Singular integral equations

The abstract Hilbert space

Bounded linear operators in Hilbert spaces

Unitary operators

Completely continuous operators in Hilbert spaces

Spectral theory for completely continuous Hermitian operators

The Sturm-Liouville eigenvalue problem

Weyl's eigenvalue problem for the Laplace operator

Some historical notices to chapter VIII

9 Linear Elliptic Differential Equations

The differential equation

The Schwarzian integral formula

The Riemann-Hilbert boundary value problem

Potential-theoretic estimates

Schauder's continuity method

Existence and regularity theorems

The Schauder estimates

Some historical notices to chapter IX

10 Weak Solutions of Elliptic Differential Equations

Sobolev spaces

Embedding and compactness

Existence of weak solutions

Boundedness of weak solutions

HSlder continuity of weak solutions

Weak potential-theoretic estimates

Boundary behavior of weak solutions

Equations in divergence form

Green's function for elliptic operators

Spectral theory of the Laplace-Beltrami operator

Some historical notices to chapter X

11 Nonlinear Partial Differential Equations

The fundamental forms and curvatures of a surface

Two-dimensional parametric integrals

Quasilinear hyperbolic differential equations and systems of second order （Characteristic parameters）

Cauchy's initial value problem for quasilinear hyperbolic

differential equations and systems of second order

Riemann's integration method

Bernstein's analyticity theorem

Some historical notices to chapter XI

12 Nonlinear Elliptic Systems

Maximum principles for the H-surface system

Gradient estimates for nonlinear elliptic systems

Global estimates for nonlinear systems

The Dirichlet problem for nonlinear elliptic systems

Distortion estimates for plane elliptic systems

A curvature estimate for minimal surfaces

Global estimates for conformal mappings with respect to Riemannian metrics

Introduction of conformal parameters into a Riemannian metric

The uniformization method for quasilinear elliptic differential equations and the Dirichlet problem

An outlook on Plateau's problem

Some historical notices to chapter XII

References

Index