内容简介

目录

作　者：（德）索维尼　著

出 版 社：世界图书出版公司

出版时间：2011-6-1

版　次：1

页　数：388

印刷时间：2011-6-1

开　本：24开

纸　张：胶版纸

印　次：1

I S B N：9787510035166

包　装：平装

内容简介

《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。目次：banach空间中的算子；hilbert空间线性算子；线性椭圆微分方程；非线性偏微分方程；非线性椭圆系统。

读者对象：数学专业的本科生，研究生和相关的科研人员。

目录

vii operators in banach spaces

1 fixed point theorems

2 the leray-schauder degree of mapping

3 fundamental properties for the degree of mapping

4 linear operators in banach spaces

5 some historical notices to the chapters iii and vii

viii linear operators in hilbert spaces

1 various eigenvalue problems

2 singular integral equations

3 the abstract hilbert space

4 bounded linear operators in hilbert spaces

5 unitary operators

6 completely continuous operators in hilbert spaces

7 spectral theory for completely continuous hermitian operators

8 the sturm-liouville eigenvalue problem

9 weyl's eigenvalue problem for the laplace operator

9 some historical notices to chapter viii

ix linear elliptic differential equations

1 the differential equation △φ+p(x, y)φx+q(x, y)φy=r(x, y)

2 the schwarzian integral formula

3 the riemann-hilbert boundary value problem

4 potential-theoretic estimates.

5 schauder's continuity method

6 existence and regularity theorems

7 the schauder estimates

8 some historical notices to chapter ix

x weak solutions of elliptic differential equations

1 sobolev spaces

2 embedding and compactness

3 existence of weak solutions

4 boundedness of weak solutions

5 hslder continuity of weak solutions

6 weak potential-theoretic estimates

7 boundary behavior of weak solutions

8 equations in divergence form

9 green's function for elliptic operators

10 spectral theory of the laplace-beltrami operator

11 some historical notices to chapter x

xi nonlinear partial differential equations

1 the fundamental forms and curvatures of a surface

2 two-dimensional parametric integrals

3 quasilinear hyperbolic differential equations and systems of second order (characteristic parameters)

4 cauchy's initial value problem for quasilinear hyperbolic differential equations and systems of second order

5 riemann's integration method

6 bernstein's analyticity theorem

7 some historical notices to chapter xi

xii nonlinear elliptic systems

1 maximum principles for the h-surface system

2 gradient estimates for nonlinear elliptic systems

3 global estimates for nonlinear systems

4 the dirichlet problem for nonlinear elliptic systems

5 distortion estimates for plane elliptic systems

6 a curvature estimate for minimal surfaces

7 global estimates for conformal mappings with respect to riemannian metrics

8 introduction of conformal parameters into a riemannian metric

9 the uniformization method for quasilinear elliptic differential equations and the dirichlet problem

10 an outlook on plateau's problem

11 some historical notices to chapter xii