04288nam 2200649 a 450 991096910850332120251002175337.01-281-07246-X97866110724690-08-054129-11-4356-0810-0(CKB)1000000000384123(EBL)316973(OCoLC)182732332(SSID)ssj0000247243(PQKBManifestationID)11237250(PQKBTitleCode)TC0000247243(PQKBWorkID)10195140(PQKB)11683769(MiAaPQ)EBC316973(PPN)151280096(EXLCZ)99100000000038412320080917d2003 uy 0engur|n|---|||||txtccrSobolev spaces /Robert A. Adams and John J.F. Fournier2nd ed.Amsterdam Academic Press20031 online resource (321 p.)Pure and applied mathematics ;v. 140Description based upon print version of record.0-12-044143-8 Includes bibliographical references and index.Front Cover; SOBOLEV SPACES; Copyright Page; CONTENTS; Preface; List of Spaces and Norms; CHAPTER 1. PRELIMINARIES; Notation; Topological Vector Spaces; Normed Spaces; Spaces of Continuous Functions; The Lebesgue Measure in Rn; The Lebesgue Integral; Distributions and Weak Derivatives; CHAPTER 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 SpacesNonimbedding Theorems for Irregular DomainsImbedding Theorems for Domains with Cusps; Imbedding Inequalities Involving Weighted Norms; Proofs of Theorems 4.51-4.53; CHAPTER 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; CHAPTER 6. COMPACT IMBEDDINGS OF SOBOLEV SPACES; The Rellich-Kondrachov Theorem; Two Counterexamples; Unbounded Domains - Compact Imbeddings of Wom'p (Ω)An Equivalent Norm for Wom'p (Ω)Unbounded Domains m Decay at Infinity; Unbounded Domains - Compact Imbeddings of W m,p (Ω); Hilbert-Schmidt Imbeddings; CHAPTER 7. FRACTIONAL ORDER SPACES; Introduction; The Bochner Integral; Intermediate Spaces and Interpolation-The Real Method; The Lorentz Spaces; Besov Spaces; Generalized Spaces of Hölder Continuous Functions; Characterization of Traces; Direct Characterizations of Besov Spaces; Other Scales of Intermediate Spaces; Wavelet Characterizations; CHAPTER 8. ORLICZ SPACES AND ORLICZ-SOBOLEV SPACES; Introduction; N-Functions; Orlicz SpacesDuality in Orlicz SpacesSeparability and Compactness Theorems; A Limiting Case of the Sobolev Imbedding Theorem; Orlicz-Sobolev Spaces; Imbedding Theorems for Orlicz-Sobolev Spaces; References; IndexSobolev 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 accPure and applied mathematics ;v. 140.Sobolev spacesSobolev spaces.510.8 s515.7510/.8 s 515/.7515.782515.782Adams Robert A.1940-27920Fournier John J. F150671MiAaPQMiAaPQMiAaPQBOOK9910969108503321Sobolev spaces474690UNINA