二阶椭圆偏微分方程(英文版) 9787506259224 世界图书出版公司 epub pdf mobi txt 电子书 下载 2024
发表于2024-11-10
二阶椭圆偏微分方程(英文版) 9787506259224 世界图书出版公司 epub pdf mobi txt 电子书 下载 2024
基本信息
书名:二阶椭圆偏微分方程(英文版)
定价:59.00元
作者:D.Gilbarg,N.S.Trudinger
出版社:世界图书出版公司
出版日期:2003-04-01
ISBN:9787506259224
字数:
页码:
版次:1
装帧:平装
开本:
商品重量:0.663kg
编辑推荐
内容提要
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 ponent 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
作者介绍
文摘
序言
二阶椭圆偏微分方程(英文版) 9787506259224 世界图书出版公司 epub pdf mobi txt 电子书 下载 2024
二阶椭圆偏微分方程(英文版) 9787506259224 世界图书出版公司 下载 epub mobi pdf txt 电子书 2024二阶椭圆偏微分方程(英文版) 9787506259224 世界图书出版公司 mobi pdf epub txt 电子书 下载 2024
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二阶椭圆偏微分方程(英文版) 9787506259224 世界图书出版公司 epub pdf mobi txt 电子书 下载 2024