# Sobolev Spaces

, eBookEnglish, 2014Edition: 2nd ed View all formats and editionsPublisher: Elsevier Science, Oxford, 2014

9780080541297, 0080541291

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(); 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. The Marcinkiewicz Interpolation TheoremCHAPTER 3. THE SOBOLEV SPACES Wm, P (); Definitions and Basic Properties; Duality and the Spaces W -m, p' (); Approximation by Smooth Functions on ; Approximation by Smooth Functions on Rn; Approximation by Functions in C0 (); Coordinate Transformations; CHAPTER 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; W m, p () as a Banach Algebra; Optimality of the Imbedding Theorem. 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 (). An 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 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