Sobolev spaces [[electronic resource] /] / Robert A. Adams and John J.F. Fournier

• Record Nr.: UNINA9910784526003321
• Autore: Adams Robert A. <1940->
• Pubbl/distr/stampa: Amsterdam, : Academic Press, 2003
• ISBN: 1-281-07246-X; 9786611072469; 0-08-054129-1; 1-4356-0810-0
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (321 p.)
• Collana: Pure and applied mathematics ; ; v. 140
• Altri autori (Persone): FournierJohn J. F
• Disciplina: 510.8 s515.7; 510/.8 s 515/.7; 515.782
• Soggetti: Sobolev spaces
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 Spaces; Nonimbedding 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 Spaces; Duality 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
• Sommario/riassunto: 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 acc