Sobo来自lev空间方面的经典专著。

• 书名 Sobolev空间
• 又名 Sobolev Spaces
• 作者 Robert A. Adams and John J.F. Fournier
• 版次  第2版

基本信息

　　图书分类: 教育/科技

　　资源格式: PDF

　　出版社: Academic Press

　　书号: 0120441438

　　发行时间: 2003年

　　地区: 美国

　　语言: 英文

内来自容简介

　　Sobolev空间方面的经典专著,也是研究偏微分方程的科研纸衣垂文落服没包阶击鸡人员必读的经典.

　　This monograph presents an introductory study of of the properties of certain Banach spaces of weakly differentiable functions of several real variable360百科s that arise in connection with numerous problems in the theory of partial differential equ离良步油仍求必ations, ap命个顾额压阳场态proximation theory, and many other areas of pure and applied mathematics. These sp孙么答凯控地围春医米aces have 凯云移测冲设洋厚心刻诉become associate造孙却连d with the name of the late Russian mathematician S. L. Sobolev, although 皇缺异their origins predate his major contributions to their development in the late 1930s.

目录

　　P五相原垂了先某安绝胞reface .

　　List of Spaces and Nor交然百混职良房ms

　　1. PRELI衡总你矿米养称龙MINARIES

　　Notation

　　Topological Vector Spaces

　　胞京尼路差车府格Normed Sp委九写aces

　　Spac种感认书师开内章es of Contin来自uous Functions

　　The Lebesgue Measure in Rn

　　The Lebesgue Integral

　　Distributions and Weak Derivatives

　　2. THE LEBESGUE SPACES LP百转(Ω)

　　Definition 目and Basic Properties

　　Completeness of Lp360百科(Ω)

　　Approximation by Continuous Functions

　　Convolutions and Young's 吗列论哪欢华扩Theorem

　　Mollifiers and Approximation by Smooth Functions

　　Precompact Sets in LP(Ω)

　　Uniform Convexity

　　The Normed D世艺洋ual of Lp(Ω)

　　Mixed-Norm Lp Spaces

　　The M进叶创古散假arcinkiewicz Interpolation Theorem

　　3. THE SOBOLEV SPACES w叫倒降美苏标必屋m,p(Ω)

　　Definitions and Basic Properties

烈应两　　Duality and the Spaces W序乱什胜影学升连山省-m,p'(Ω)

　　Approximation by Smooth Functions on Ω

　　Approximation by Smooth Functions on Rn

　　A路求坚茶坐坚面逐pproximation by Functions in C0∞ (Ω)

　　Coordinate T句论起较弦乎沿地封ransformations

　　4. THE SOBOLEV IMBEDDING THEOREM

　　Geometric Properties of Domains

　　Imbeddings by Potential Arguments

　　Imbeddings by Averaging

　　Imbedd集倍独管改ings into Lipschitz Spaces

　　Sobolev's Inequality

　　Variations of Sobolev's Inequality

　　wm'p(Ω) as a Banach 板双看误教庆向留室每Algebra

　　Optimality of the Imbedding Theorem

　　Nonimbedding Theorems for Irregular Domains ..

　　Imbedding Theorems for Domains with Cusps

　　Imbedding Inequalities Involving Weighted Norms

　　Proofs of Theorems 4.51-4.53

　　5. INTERPOLATION, EXTENSION, AND APPROXIMATION

　　THEOREMS

　　Interpolation on Order of Smoothness

　　Interpolation on Degree of Sumability

　　Interpolation Involving Compact Subdomains

　　Extension Theorems

　　An Approximation Theorem

　　Boundary Traces

　　6. COMPACT IMBEDDINGS OF SOBOLEV SPACES

　　The Rellich-Kondrachov Theorem

　　Two Counterexamples

　　Unbounded Domains -- Compact Imbeddings of W0m,p (Ω)

　　An Equivalent Norm for W0m,P(Ω)

　　Unbounded Domains -- Decay at Infinity

　　Unbounded Domains -- Compact Imbeddings of Wm,p (Ω)

　　Hilbert-Schmidt Imbeddings

　　7. FRACTIONAL ORDER SPACES

　　Introduction

　　The Bochner Integral

　　Intermediate Spaces and Interpolation -- The Real Method

　　The Lorentz Spaces

　　Besov Spaces

　　Generalized Spaces of H61der Continuous Functions

　　Characterization of Traces

　　Direct Characterizations 9f Besov Spaces

　　Other Scales of Intermediate Spaces

　　Wavelet Characterizations

　　8. ORLICZ SPACES AND ORLICZ-SOBOLEV SPACES

　　Introduction

　　N-Functions

　　Orlicz Spaces

　　Duality in Orlicz Spaces

　　Separability and Compactness Theorems

　　A Limiting Case of the Sobolev Imbedding Theorem

　　Orlicz-Sobolev Spaces

　　Imbedding Theorems for Orlicz-Sobolev Spaces

　　References

　　Index