Sobolev空间 Sobolev Spaces Robert A. Adams and John J.F. Fournier 第2版[PDF]

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资源信息： 中文名: Sobolev空间 原名: Sobolev Spaces 作者: Robert A. Adams and John J.F. Fournier 资源格式: PDF 版本: 第2版 出版社: Academic Press 书号: 0120441438 发行时间: 2003年 地区: 美国 语言: 英文 概述:

内容简介: This monograph presents an introductory study of of the properties of certain Banach spaces of weakly differentiable functions of several real variables that arise in connection with numerous problems in the theory of partial differential equations, approximation theory, and many other areas of pure and applied mathematics. These spaces have become associated with the name of the late Russian mathematician S. L. Sobolev, although their origins predate his major contributions to their development in the late 1930s. 内容截图:

目录: Preface . List of Spaces and Norms 1. PRELIMINARIES Notation Topological Vector Spaces Normed Spaces Spaces of Continuous Functions The Lebesgue Measure in Rn The Lebesgue Integral Distributions and Weak Derivatives 2. THE LEBESGUE SPACES LP(Ω) Definition and Basic Properties Completeness of Lp(Ω) Approximation by Continuous Functions Convolutions and Young's Theorem Mollifiers and Approximation by Smooth Functions Precompact Sets in LP(Ω) Uniform Convexity The Normed Dual of Lp(Ω) Mixed-Norm Lp Spaces The Marcinkiewicz Interpolation Theorem 3. THE SOBOLEV SPACES wm,p(Ω) Definitions and Basic Properties Duality and the Spaces W-m,p'(Ω) Approximation by Smooth Functions on Ω Approximation by Smooth Functions on Rn Approximation by Functions in C0∞ (Ω) Coordinate Transformations 4. THE SOBOLEV IMBEDDING THEOREM Geometric Properties of Domains Imbeddings by Potential Arguments Imbeddings by Averaging Imbeddings into Lipschitz Spaces Sobolev's Inequality Variations of Sobolev's Inequality wm'p(Ω) as a Banach 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