Sobolev spaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam ; Boston ; Heidelberg ; London ; New York ; Oxford ; Paris ; San Diego ; San Francisco ; Singapore ; Sydney ; Tokyo
Academic Press
2003
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Pure and applied mathematics
140 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xiii, 305 Seiten Diagramme |
| ISBN: | 0120441438 9780120441433 |
Internformat
MARC
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| 100 | 1 | |a Adams, Robert A. |d 1940- |0 (DE-588)141723874 |4 aut | |
| 245 | 1 | 0 | |a Sobolev spaces |c Robert A. Adams and John J. F. Fournier ; Department of Mathematics ; The University of British Columbia ; Vancuver, Canada |
| 250 | |a Second Edition | ||
| 264 | 1 | |a Amsterdam ; Boston ; Heidelberg ; London ; New York ; Oxford ; Paris ; San Diego ; San Francisco ; Singapore ; Sydney ; Tokyo |b Academic Press |c 2003 | |
| 300 | |a xiii, 305 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 140 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Espaços de sobolev |2 larpcal | |
| 650 | 4 | |a Sobolev spaces | |
| 650 | 0 | 7 | |a Sobolev-Raum |0 (DE-588)4055345-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Sobolev-Raum |0 (DE-588)4055345-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Fournier, John J. F. |0 (DE-588)141723939 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |w (DE-604)BV036962376 |
| 830 | 0 | |a Pure and applied mathematics |v 140 |w (DE-604)BV010177228 |9 140 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-012032527 | ||
Datensatz im Suchindex
| _version_ | 1804131848254652416 |
|---|---|
| adam_text | CONTENTS
Preface
ix
List of Spaces and Norms
xii
1.
PRELIMINARIES
1
Notation
1
Topological Vector Spaces
3
Normed Spaces
4
Spaces of Continuous Functions
Ю
The Lebesgue Measure in R
13
The Lebesgue Integral
16
Distributions and Weak Derivatives
19
2.
THE LEBESGUE SPACES
ЩО)
23
Definition and Basic Properties
23
Completeness of
Ζ/(Ω) 29
Approximation by Continuous Functions
31
Convolutions and Young s Theorem
32
Mollifiers and Approximation by Smooth Functions
36
Precompact Sets in LP(Q)
38
Uniform Convexity
41
The Normed Dual of
U
(Ω) 45
Mixed-Norm Lp Spaces 49
The Marcinkiewicz Interpolation Theorem
52
vi
Contents
3.
THE SOBOLEV SPACES Wm*{O)
59
Definitions and Basic Properties
59
Duality and the Spaces W~m-p
(Ω)
62
Approximation by Smooth Functions on
Ω
65
Approximation by Smooth Functions on
Шп
67
Approximation by Functions in
Ο^°(Ω)
70
Coordinate Transformations
77
4.
THE SOBOLEV IMBEDDING THEOREM
79
Geometric Properties of Domains
81
Imbeddings by Potential Arguments
87
Imbeddings by Averaging
93
Imbeddings into Lipschitz Spaces
99
Sobolev s Inequality
101
Variations of Sobolev s Inequality
104
Wm
Ρ(Ω)
as a Banach Algebra
106
Optimality of the Imbedding Theorem
108
Nonimbedding Theorems for Irregular Domains
111
Imbedding Theorems for Domains with Cusps
115
Imbedding Inequalities Involving Weighted Norms
119
Proofs of Theorems
4.51^.53 131
5.
INTERPOLATION, EXTENSION, AND APPROXIMATION
135
THEOREMS
Interpolation on Order of Smoothness
135
Interpolation on Degree of Sumability
139
Interpolation Involving Compact
Subdomains
143
Extension Theorems
146
An Approximation Theorem
159
Boundary Traces
163
6.
COMPACT IMBEDDINGS OF SOBOLEV SPACES
167
The Rellich-Kondrachov Theorem
167
Two Counterexamples
173
Unbounded Domains
—
Compact Imbeddings of
Wq p(Q)
175
An Equivalent Norm for Wq p(Q)
183
Unbounded Domains
—
Decay at Infinity
186
Unbounded Domains
—
Compact Imbeddings of Wm
·
p
(
Ω)
195
Hiibert-Schmidt Imbeddings
200
Contents
vii
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
Sobofev
&>рі&ся&&
presents an introduction to the theory of Sobotev spaces
spaces of function of
severei
treat variabiee, especially the Imbedding char^ctefistJcs of
limese
spaces. This theory is
vzdory
used in Pure and Applied
fvfetfhemafäes
and the
Physical Sciences.
This second ec&tion of Adams* ckss&sac reference text contains many additions and much
modernizing and refining of material The basic premise of the book remains unchanged:
is intended to provide a solid foundation
m
these spacers fbr graduate
students and researchers afcke.
Seif
-contained and accessibie for readers in other
cšscipíines.
Written at eiementary
łeveJ
making it accessible to graduate students.
Includes reviews of reak analysis and an extensive treatment of Lebesgue spaces.
Develops at length the intrinsic definition and properties of Soboiev spaces, in
particular
their imbedding, compact imfoeddirtg, interpolation and extension properties.
Provides a thorough treatment of the
reaí interpofatíon
rrtsthod and its application to
Lorentz
and
Besov
spaces
.
Includes surveys of other fractional-order spaces
(Besseł
potentiate, Tnebel-Lizorkin).
Develops the theory of OHicz and Oucz-Sobolev spaces and their imbeddings.
A· Atdhmmm is Professor Emeritus
oř
Mathematics a* The University of
British
Coharrrxa.
where he has taught since
1966.
His research interests began in
Parttal
Offeren
tiaí
Equations end
rrngraíed
to
rrbeddtnçjs
Ы
Soboiev Spaces. His
łaiter
work led to the first edition
oř
this book Lefcer.
he wrote
a series
of Caicubs
beote,
now in their fifth editions. He ts now joined by John J. F. Fournter
to prepare th»s second edition.
JL K.
&€miF!&âmir
is Professor of Mathematics at The University of British Columbia.* where he
taucht
sinea
1967.
His research area» ere Fourier Aneiy&iS and Function Spaces. He served as
co-Hdfoor-in-Chief
of the Canecaan Mathematical
|
| any_adam_object | 1 |
| author | Adams, Robert A. 1940- Fournier, John J. F. |
| author_GND | (DE-588)141723874 (DE-588)141723939 |
| author_facet | Adams, Robert A. 1940- Fournier, John J. F. |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.782 |
| dewey-search | 515.782 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Second Edition |
| format | Book |
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| id | DE-604.BV019268867 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:43:27Z |
| institution | BVB |
| isbn | 0120441438 9780120441433 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012032527 |
| oclc_num | 52824266 |
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| owner_facet | DE-824 DE-91G DE-BY-TUM DE-11 DE-83 DE-355 DE-BY-UBR |
| physical | xiii, 305 Seiten Diagramme |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Academic Press |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Adams, Robert A. 1940- (DE-588)141723874 aut Sobolev spaces Robert A. Adams and John J. F. Fournier ; Department of Mathematics ; The University of British Columbia ; Vancuver, Canada Second Edition Amsterdam ; Boston ; Heidelberg ; London ; New York ; Oxford ; Paris ; San Diego ; San Francisco ; Singapore ; Sydney ; Tokyo Academic Press 2003 xiii, 305 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 140 Hier auch später erschienene, unveränderte Nachdrucke Espaços de sobolev larpcal Sobolev spaces Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 s DE-604 Fournier, John J. F. (DE-588)141723939 aut Erscheint auch als Online-Ausgabe (DE-604)BV036962376 Pure and applied mathematics 140 (DE-604)BV010177228 140 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012032527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012032527&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Adams, Robert A. 1940- Fournier, John J. F. Sobolev spaces Pure and applied mathematics Espaços de sobolev larpcal Sobolev spaces 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_full | Sobolev spaces Robert A. Adams and John J. F. Fournier ; Department of Mathematics ; The University of British Columbia ; Vancuver, Canada |
| title_fullStr | Sobolev spaces Robert A. Adams and John J. F. Fournier ; Department of Mathematics ; The University of British Columbia ; Vancuver, Canada |
| title_full_unstemmed | Sobolev spaces Robert A. Adams and John J. F. Fournier ; Department of Mathematics ; The University of British Columbia ; Vancuver, Canada |
| title_short | Sobolev spaces |
| title_sort | sobolev spaces |
| topic | Espaços de sobolev larpcal Sobolev spaces Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Espaços de sobolev Sobolev spaces Sobolev-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012032527&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012032527&sequence=000005&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010177228 |
| work_keys_str_mv | AT adamsroberta sobolevspaces AT fournierjohnjf sobolevspaces |