LEADER 04291nam 2200637 a 450 001 9910784526003321 005 20200123190918.0 010 $a1-281-07246-X 010 $a9786611072469 010 $a0-08-054129-1 010 $a1-4356-0810-0 035 $a(CKB)1000000000384123 035 $a(EBL)316973 035 $a(OCoLC)182732332 035 $a(SSID)ssj0000247243 035 $a(PQKBManifestationID)11237250 035 $a(PQKBTitleCode)TC0000247243 035 $a(PQKBWorkID)10195140 035 $a(PQKB)11683769 035 $a(MiAaPQ)EBC316973 035 $a(PPN)151280096 035 $a(EXLCZ)991000000000384123 100 $a20080917d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSobolev spaces$b[electronic resource] /$fRobert A. Adams and John J.F. Fournier 205 $a2nd ed. 210 $aAmsterdam $cAcademic Press$d2003 215 $a1 online resource (321 p.) 225 1 $aPure and applied mathematics ;$vv. 140 300 $aDescription based upon print version of record. 311 $a0-12-044143-8 320 $aIncludes bibliographical references and index. 327 $aFront 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(?)?; Definition and Basic Properties; Completeness of LP (?)?; Approximation by Continuous Functions; Convolutions and Young's Theorem; Mollifiers and Approximation by Smooth Functions; Precompact Sets in LP (?); Uniform Convexity; The Normed Dual of LP (?); Mixed-Norm LP Spaces 327 $aNonimbedding 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 (?) 327 $aAn Equivalent Norm for Wom'p (?)Unbounded Domains m Decay at Infinity; Unbounded Domains - Compact Imbeddings of W m,p (?); 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 Ho?lder 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 Spaces 327 $aDuality in Orlicz SpacesSeparability and Compactness Theorems; A Limiting Case of the Sobolev Imbedding Theorem; Orlicz-Sobolev Spaces; Imbedding Theorems for Orlicz-Sobolev Spaces; References; Index 330 $aSobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.* Self-contained and acc 410 0$aPure and applied mathematics ;$vv. 140. 606 $aSobolev spaces 615 0$aSobolev spaces. 676 $a510.8 s515.7 676 $a510/.8 s 515/.7 676 $a515.782 700 $aAdams$b Robert A.$f1940-$027920 701 $aFournier$b John J. F$0150671 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784526003321 996 $aSobolev spaces$9474690 997 $aUNINA