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Sobolev spaces:

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Main Authors:	Adams, Robert A. 1940- (Author), Fournier, John J. F. (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Acad. Press 2008
Edition:	2. ed., reprint.
Series:	Pure and applied mathematics 140
Subjects:	Sobolev-Raum
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XIII, 305 S. graph. Darst.
ISBN:	0120441438 9780120441433 9780123958419

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MARC


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adam_text	CONTENTS Preface List of Spaces and Norms 1. PRELIMINARIES Notation Topological Vector Spaces Normed Spaces Spaces of Continuous Functions The Lebesgue Measure in W The Lebesgue Integral Distributions and Weak Derivatives 2. THE LEBESGUE SPACES Definition and Basic Properties Completeness of ¿Ρ(Ω) Approximation by Continuous Functions Convolutions and Young s Theorem Mollifiers and Approximation by Smooth Functions Precompact Sets in LP{Q) Uniform Convexity The Normed Dual of U (Ω) Mixed-Norm Lp Spaces The Marcinkiewicz Interpolation Theorem 3. THE SOBOLEV SPACES Definitions and Basic Properties Duality and the Spaces W~m-P (Q) Approximation by Smooth Functions on Ω Approximation by Smooth Functions on Ж Approximation by Functions in (Γ^°(Ω) Coordinate Transformations 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 Wm P(u) as a Banach Algebra Optimality of the Imbedding Theorem Nonimbedding Theorems for Irregular Domains Imbedding Theorems for Domains with Cusps Imbedding Inequalities Involving Weighted Norms Proofs of Theorems 4.51-4.53 5. INTERPOLATION, EXTENSION, AND APPROXIMATION 135 THEOREMS Interpolation on Order of Smoothness Interpolation on Degree of Sumability Interpolation Involving Compact Subdomains Extension Theorems An Approximation Theorem Boundary Traces 6. COMPACT IMBEDDINGS OF SOBOLEV SPACES 167 The Rellich-Kondrachov Theorem 167 Two Counterexamples 173 Unbounded Domains — Compact Imbeddings of W 1 (Ω) 175 An Equivalent Norm for Ψ™·Ρ(Ω) 183 Unbounded Domains — Decay at Infinity 186 Unbounded Domains — Compact Imbeddings of Wm p (Ω) 195 Hilbert-Schmidt Imbeddings 200 7. FRACTIONAL ORDER SPACES 205 Introduction 205 The Bochner Integral 206 Intermediate Spaces and Interpolation — The Real Method 208 The Lorentz Spaces 221 Besov Spaces 228 Generalized Spaces of Holder Continuous Functions 232 Characterization of Traces 234 Direct Characterizations of Besov Spaces 241 Other Scales of Intermediate Spaces 247 Wavelet Characterizations 256 8. ORLICZ SPACES AND ORLICZ-SOBOLEV SPACES 261 Introduction 261 N-Functions 262 Orlicz Spaces 266 Duality in Orlicz Spaces 272 Separability and Compactness Theorems 274 A Limiting Case of the Sobolev Imbedding Theorem 277 Orlicz-Sobolev Spaces 281 Imbedding Theorems for Orlicz-Sobolev Spaces 282 References 295 Index 301
adam_txt	CONTENTS Preface List of Spaces and Norms 1. PRELIMINARIES Notation Topological Vector Spaces Normed Spaces Spaces of Continuous Functions The Lebesgue Measure in W The Lebesgue Integral Distributions and Weak Derivatives 2. THE LEBESGUE SPACES Definition and Basic Properties Completeness of ¿Ρ(Ω) Approximation by Continuous Functions Convolutions and Young's Theorem Mollifiers and Approximation by Smooth Functions Precompact Sets in LP{Q) Uniform Convexity The Normed Dual of U (Ω) Mixed-Norm Lp Spaces The Marcinkiewicz Interpolation Theorem 3. THE SOBOLEV SPACES Definitions and Basic Properties Duality and the Spaces W~m-P'(Q) Approximation by Smooth Functions on Ω Approximation by Smooth Functions on Ж" Approximation by Functions in (Γ^°(Ω) Coordinate Transformations 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 Wm'P(u) as a Banach Algebra Optimality of the Imbedding Theorem Nonimbedding Theorems for Irregular Domains Imbedding Theorems for Domains with Cusps Imbedding Inequalities Involving Weighted Norms Proofs of Theorems 4.51-4.53 5. INTERPOLATION, EXTENSION, AND APPROXIMATION 135 THEOREMS Interpolation on Order of Smoothness Interpolation on Degree of Sumability Interpolation Involving Compact Subdomains Extension Theorems An Approximation Theorem Boundary Traces 6. COMPACT IMBEDDINGS OF SOBOLEV SPACES 167 The Rellich-Kondrachov Theorem 167 Two Counterexamples 173 Unbounded Domains — Compact Imbeddings of W"'1' (Ω) 175 An Equivalent Norm for Ψ™·Ρ(Ω) 183 Unbounded Domains — Decay at Infinity 186 Unbounded Domains — Compact Imbeddings of Wm'p (Ω) 195 Hilbert-Schmidt Imbeddings 200 7. FRACTIONAL ORDER SPACES 205 Introduction 205 The Bochner Integral 206 Intermediate Spaces and Interpolation — The Real Method 208 The Lorentz Spaces 221 Besov Spaces 228 Generalized Spaces of Holder Continuous Functions 232 Characterization of Traces 234 Direct Characterizations of Besov Spaces 241 Other Scales of Intermediate Spaces 247 Wavelet Characterizations 256 8. ORLICZ SPACES AND ORLICZ-SOBOLEV SPACES 261 Introduction 261 N-Functions 262 Orlicz Spaces 266 Duality in Orlicz Spaces 272 Separability and Compactness Theorems 274 A Limiting Case of the Sobolev Imbedding Theorem 277 Orlicz-Sobolev Spaces 281 Imbedding Theorems for Orlicz-Sobolev Spaces 282 References 295 Index 301
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author	Adams, Robert A. 1940- Fournier, John J. F.
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index_date	2024-07-02T21:53:04Z
indexdate	2024-07-09T21:20:50Z
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isbn	0120441438 9780120441433 9780123958419
language	English
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physical	XIII, 305 S. graph. Darst.
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series	Pure and applied mathematics
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spelling	Adams, Robert A. 1940- Verfasser (DE-588)141723874 aut Sobolev spaces Robert A. Adams and John J. F. Fournier 2. ed., reprint. Amsterdam [u.a.] Acad. Press 2008 XIII, 305 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 140 Hier auch später erschienene, unveränderte Nachdrucke Sobolev-Raum Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 s DE-604 Fournier, John J. F. Verfasser (DE-588)141723939 aut Pure and applied mathematics 140 (DE-604)BV010177228 140 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016709858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Adams, Robert A. 1940- Fournier, John J. F. Sobolev spaces Pure and applied mathematics Sobolev-Raum Sobolev-Raum (DE-588)4055345-0 gnd
subject_GND	(DE-588)4055345-0
title	Sobolev spaces
title_auth	Sobolev spaces
title_exact_search	Sobolev spaces
title_exact_search_txtP	Sobolev spaces
title_full	Sobolev spaces Robert A. Adams and John J. F. Fournier
title_fullStr	Sobolev spaces Robert A. Adams and John J. F. Fournier
title_full_unstemmed	Sobolev spaces Robert A. Adams and John J. F. Fournier
title_short	Sobolev spaces
title_sort	sobolev spaces
topic	Sobolev-Raum Sobolev-Raum (DE-588)4055345-0 gnd
topic_facet	Sobolev-Raum
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016709858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV010177228
work_keys_str_mv	AT adamsroberta sobolevspaces AT fournierjohnjf sobolevspaces

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