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　　分類: 图书,科学与自然,数学,数学分析,

基本信息·出版社：世界图书出版公司

·页码：517200341 页

·出版日期：2003年

·ISBN：7506259222

·条形码：9787506259224

·包装版本：2003年4月第1版

·装帧：平装

·开本：24开

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内容简介This revision of the 1983 second edition of"Elliptic Partial Differential Equations of Second Order" corresponds to the Russian edition, published in 1989, in which we essentially updated the previous version to 1984. The additional text relates to the boundary H61der derivative estimates of Nikolai Krylov, which provided a fundamental component of the further development of the classical theory of elliptic (and parabolic), fully nonlinear equations in higher dimensions. In our presentation we adapted a simplification of Krylov's approach due to Luis Caffarelli.

编辑推荐This revision of the 1983 second edition of"Elliptic Partial Differential Equations of Second Order" corresponds to the Russian edition, published in 1989, in which we essentially updated the previous version to 1984. The additional text relates to the boundary H61der derivative estimates of Nikolai Krylov, which provided a fundamental component of the further development of the classical theory of elliptic (and parabolic), fully nonlinear equations in higher dimensions. In our presentation we adapted a simplification of Krylov's approach due to Luis Caffarelli.

目录

Chapter 1. Introduction

Part Ⅰ Linear Equations

Chapter 2 Laplace’s Equation

2.1 The Mean Value Inequalities

2.2 Maximum and Minimum Principle

2.3 The Harnack Inequality

2.4 Green’s Representation

2.5 The Poisson Integral

2.6 Convergence Theorems

2.7 Interior Estimates of Derivatives

2.8 The Dirichlet Problem； the Method of Subharmonic Functions

2.9 Capacity

Problems

Chapter 3 The Classical Maximum Principle

3.1 The Weak Maximum Principle

3.2 The Strong Maximum Principle

3.3 Apriori Bounds

3.4 Gradient Estimates for Poisson’s Equation

3.5 A Harnack Inequality

3.6 Operators in Divergence Form

Notes

Problems

Chapter 4 Poisson's Equation and the Newtonian Potential

4.1 Holder Continuity

4.2 The Dirichlet Problem for Poisson's Equation

4.3 Holder Estimates for the Second Derivatives

4.4 Eximates at the Boundary

4.5 Holder Estimates for the First Derivatives

Notes

Problems

Chapter 5 Banach and Hilbert Spaces

5.1 The Contraction Mapping Principle

5.2 The Method of Continity

5.3 The Fredholm Alternative

5.4 Dual Spaces and Adjoints

5.5 Hilbert Spaces

5.6 The Projection Theorem

5.7 The Riesz Represenation Theorem

5.8 The Lax-Milgram Theorem

5.9 The Fredholm Alternative in Hilbert Spaces

5.10 Weak Compactness

Notes

Problems

Chapter 6 Calssical Solutions; the Schauder Approach

Chapter 7 Sobolev Spaces

Chapter 8 Generalized Solutiona and regularity

Chapter 9 Strong Solutions

Part Ⅱ Quasilinear Equations

Chapter 10 Maximum and Comparison Principles

Chapter 11 Topological Fixed Point Theorems and Their Application

Chapter 12 Equation in Two Varables

Chapter 13 Holder Extimates for the Cradient

Chapter 14 Boundary Gradient Estimates

Chapter 15 Global and Interior Gradient Bounds

Chapter 16 Equations of Mean Curvature Type

Chapter 17 Fully Nonlinear Equations

Bibliography

Epilogue

Subject Index

Notation Index

……[看更多目录]

 

 

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