Sobolev spaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Acad. Press
2006
|
| Ausgabe: | 2. ed., reprint. |
| Schriftenreihe: | Pure and applied mathematics
140 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 305 S. graph. Darst. |
| ISBN: | 0120441438 |
Internformat
MARC
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| 100 | 1 | |a Adams, Robert A. |d 1940- |e Verfasser |0 (DE-588)141723874 |4 aut | |
| 245 | 1 | 0 | |a Sobolev spaces |c Robert A. Adams and John J. F. Fournier |
| 250 | |a 2. ed., reprint. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Acad. Press |c 2006 | |
| 300 | |a XIII, 305 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Pure and applied mathematics |v 140 | |
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Datensatz im Suchindex
| _version_ | 1804136612418813952 |
|---|---|
| adam_text | CONTENTS
Preface ¡x
List of Spaces and Norms
1.
Notation
Topological Vector Spaces
Normed Spaces
Spaces of Continuous Functions
The Lebesgue Measure in ft
The Lebesgue Integral
Distributions and Weak Derivatives
2.
Definition and Basic Properties
Completeness of LP(Q)
Approximation by Continuous Functions
Convolutions and Young s Theorem
Mollifiers and Approximation by Smooth Functions
Precompact Sets in
Uniform Convexity
The Normed Dual of
Mixed-Norm Lp Spaces
The Marcinkiewicz Interpolation Theorem
vi
3.
Definitions and Basic Properties
Duality and the Spaces W~m-p
Approximation by Smooth Functions on
Approximation by Smooth Functions on M
Approximation by Functions in
Coordinate Transformations
4.
Geometric Properties of Domains
Imbeddings by Potential Arguments
Imbeddings by Averaging
Imbeddings into Lipschitz Spaces
Sobolev s Inequality
Variations of Sobolev s Inequality
ψ ·ρ(Ω)
Optimality of the Imbedding Theorem
Nonimbedding Theorems for Irregular Domains
Imbedding Theorems for Domains with Cusps
Imbedding Inequalities Involving Weighted Norms
Proofs of Theorems
5.
THEOREMS
Interpolation on Order of Smoothness
Interpolation on Degree of Sumability
Interpolation Involving Compact
Extension Theorems
An Approximation Theorem
Boundary Traces
6.
The Rellich-Kondrachov Theorem
Two Counterexamples
Unbounded Domains
An Equivalent Norm for
Unbounded Domains
Unbounded Domains
Hilbert-Schmidt Imbeddings
vi
Contents
7.
Introduction
The Bochner Integral
Intermediate Spaces and Interpolation
The
Besov
Generalized Spaces of Holder Continuous Functions
Characterization of Traces
Direct Characterizations of
Other Scales of Intermediate Spaces
Wavelet Characterizations
8.
Introduction
N-Functions
Orlicz Spaces
Duality in Orlicz Spaces
Separability and Compactness Theorems
A Limiting Case of the Sobolev Imbedding Theorem
Orlicz-Sobolev Spaces
Imbedding Theorems for Orlicz-Sobolev Spaces
References
Index
|
| adam_txt |
CONTENTS
Preface ¡x
List of Spaces and Norms
1.
Notation
Topological Vector Spaces
Normed Spaces
Spaces of Continuous Functions
The Lebesgue Measure in ft"
The Lebesgue Integral
Distributions and Weak Derivatives
2.
Definition and Basic Properties
Completeness of LP(Q)
Approximation by Continuous Functions
Convolutions and Young's Theorem
Mollifiers and Approximation by Smooth Functions
Precompact Sets in
Uniform Convexity
The Normed Dual of
Mixed-Norm Lp Spaces
The Marcinkiewicz Interpolation Theorem
vi
3.
Definitions and Basic Properties
Duality and the Spaces W~m-p'
Approximation by Smooth Functions on
Approximation by Smooth Functions on M"
Approximation by Functions in
Coordinate Transformations
4.
Geometric Properties of Domains
Imbeddings by Potential Arguments
Imbeddings by Averaging
Imbeddings into Lipschitz Spaces
Sobolev's Inequality
Variations of Sobolev's Inequality
ψ'"·ρ(Ω)
Optimality of the Imbedding Theorem
Nonimbedding Theorems for Irregular Domains
Imbedding Theorems for Domains with Cusps
Imbedding Inequalities Involving Weighted Norms
Proofs of Theorems
5.
THEOREMS
Interpolation on Order of Smoothness
Interpolation on Degree of Sumability
Interpolation Involving Compact
Extension Theorems
An Approximation Theorem
Boundary Traces
6.
The Rellich-Kondrachov Theorem
Two Counterexamples
Unbounded Domains
An Equivalent Norm for
Unbounded Domains
Unbounded Domains
Hilbert-Schmidt Imbeddings
vi
Contents
7.
Introduction
The Bochner Integral
Intermediate Spaces and Interpolation
The
Besov
Generalized Spaces of Holder Continuous Functions
Characterization of Traces
Direct Characterizations of
Other Scales of Intermediate Spaces
Wavelet Characterizations
8.
Introduction
N-Functions
Orlicz Spaces
Duality in Orlicz Spaces
Separability and Compactness Theorems
A Limiting Case of the Sobolev Imbedding Theorem
Orlicz-Sobolev Spaces
Imbedding Theorems for Orlicz-Sobolev Spaces
References
Index |
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| author | Adams, Robert A. 1940- Fournier, John J. F. |
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| ctrlnum | (OCoLC)255893745 (DE-599)BVBBV022510025 |
| dewey-full | 515.782 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.782 |
| dewey-search | 515.782 |
| dewey-sort | 3515.782 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed., reprint. |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T17:59:04Z |
| indexdate | 2024-07-09T20:59:10Z |
| institution | BVB |
| isbn | 0120441438 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015716956 |
| oclc_num | 255893745 |
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| physical | XIII, 305 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Acad. Press |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| 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 2006 XIII, 305 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 140 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 Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015716956&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=015716956&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 |