فضاهای سوبولف، ویرایش دوم (ریاضیات خالص و کاربردی، جلد ۱۴۰)

Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences. This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike. * Self-contained and accessible for readers in other disciplines. * Written at elementary level making it accessible to graduate students. Front Cover......Page 1 SOBOLEV SPACES......Page 4 Copyright Page......Page 5 CONTENTS......Page 6 Preface......Page 10 List of Spaces and Norms......Page 13 Notation......Page 16 Topological Vector Spaces......Page 18 Normed Spaces......Page 19 Spaces of Continuous Functions......Page 25 The Lebesgue Measure in Rn......Page 28 The Lebesgue Integral......Page 31 Distributions and Weak Derivatives......Page 34 Definition and Basic Properties......Page 38 Completeness of LP (Ώ)......Page 44 Approximation by Continuous Functions......Page 46 Convolutions and Young's Theorem......Page 47 Mollifiers and Approximation by Smooth Functions......Page 51 Precompact Sets in LP (Ω)......Page 53 Uniform Convexity......Page 56 The Normed Dual of LP (Ω)......Page 60 Mixed-Norm LP Spaces......Page 64 The Marcinkiewicz Interpolation Theorem......Page 67 Definitions and Basic Properties......Page 74 Duality and the Spaces W -m,p' (Ω)......Page 77 Approximation by Smooth Functions on Ω......Page 80 Approximation by Smooth Functions on Rn......Page 82 Approximation by Functions in C0∞ (Ω)......Page 85 Coordinate Transformations......Page 92 CHAPTER 4. THE SOBOLEV IMBEDDING THEOREM......Page 94 Geometric Properties of Domains......Page 96 Imbeddings by Potential Arguments......Page 102 Imbeddings by Averaging......Page 108 Imbeddings into Lipschitz Spaces......Page 114 Sobolev's Inequality......Page 116 Variations of Sobolev's Inequality......Page 119 W m,p (Ω) as a Banach Algebra......Page 121 Optimality of the Imbedding Theorem......Page 123 Nonimbedding Theorems for Irregular Domains......Page 126 Imbedding Theorems for Domains with Cusps......Page 130 Imbedding Inequalities Involving Weighted Norms......Page 134 Proofs of Theorems 4.51–4.53......Page 146 Interpolation on Order of Smoothness......Page 150 Interpolation on Degree of Sumability......Page 154 Interpolation Involving Compact Subdomains......Page 158 Extension Theorems......Page 161 An Approximation Theorem......Page 174 Boundary Traces......Page 178 The Rellich-Kondrachov Theorem......Page 182 Two Counterexamples......Page 188 Unbounded Domains — Compact Imbeddings of Wom'p (Ω)......Page 190 An Equivalent Norm for Wom'p (Ω)......Page 198 Unbounded Domains m Decay at Infinity......Page 201 Unbounded Domains — Compact Imbeddings of W m,p (Ω)......Page 210 Hilbert-Schmidt Imbeddings......Page 215 Introduction......Page 220 The Bochner Integral......Page 221 Intermediate Spaces and Interpolation—The Real Method......Page 223 The Lorentz Spaces......Page 236 Besov Spaces......Page 243 Generalized Spaces of Hölder Continuous Functions......Page 247 Characterization of Traces......Page 249 Direct Characterizations of Besov Spaces......Page 256 Other Scales of Intermediate Spaces......Page 262 Wavelet Characterizations......Page 271 Introduction......Page 276 N-Functions......Page 277 Orlicz Spaces......Page 281 Duality in Orlicz Spaces......Page 287 Separability and Compactness Theorems......Page 289 A Limiting Case of the Sobolev Imbedding Theorem......Page 292 Orlicz-Sobolev Spaces......Page 296 Imbedding Theorems for Orlicz-Sobolev Spaces......Page 297 References......Page 310 Index......Page 316 Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.

This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.

* Self-contained and accessible for readers in other disciplines.
* Written at elementary level making it accessible to graduate students.