Concentration compactness: functional-analytic theory of concentration phenomena
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin : Boston
De Gruyter
[2020]
|
| Series: | De Gruyter series in nonlinear analysis and applications
volume 33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XI, 216 Seiten 25 cm, 544 g |
| ISBN: | 9783110530346 3110530341 |
Staff View
MARC
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| 020 | |a 3110530341 |c hardcover |9 3-11-053034-1 | ||
| 024 | 3 | |a 9783110530346 | |
| 035 | |a (OCoLC)1124325772 | ||
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| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Tintarev, Kyril |d 1956- |e Verfasser |0 (DE-588)1205670777 |4 aut | |
| 245 | 1 | 0 | |a Concentration compactness |b functional-analytic theory of concentration phenomena |c Cyril Tintarev |
| 264 | 1 | |a Berlin : Boston |b De Gruyter |c [2020] | |
| 300 | |a XI, 216 Seiten |c 25 cm, 544 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter series in nonlinear analysis and applications |v volume 33 | |
| 650 | 0 | 7 | |a Kompaktheit |0 (DE-588)4456100-3 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Einbettung |g Mathematik |0 (DE-588)4151233-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Folge |g Mathematik |0 (DE-588)4017790-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 653 | |a Funktionalanalysis | ||
| 653 | |a Kompaktheit | ||
| 653 | |a Nichtlineare elliptische Differentialgleichung | ||
| 653 | |a Nichtlineare Funktionalanalysis | ||
| 653 | |a Schwache Konvergenz | ||
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Record in the Search Index
| _version_ | 1804181304847106048 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
VII
1
PROFILE
DECOMPOSITION:
A
STRUCTURED
DEFECT
OF
COMPACTNESS
*
1
1.1
COCOMPACT
EMBEDDINGS:
DEFINITION
AND
EXAMPLES
*
1
1.2
PROFILE
DECOMPOSITION
*
5
1.3
BREZIS-LIEB
LEMMA
*
7
1.4
LIONS
*
LEMMA
FOR
THE
MOSER-TRUDINGER
FUNCTIONAL
*
11
1.5
BIBLIOGRAPHIC
NOTES
*
13
2
DELTA-CONVERGENCE
AND
WEAK
CONVERGENCE
*
15
2.1
DEFINITION
OF
DELTA-CONVERGENCE
*
15
2.2
CHEBYSHEV
AND
ASYMPTOTIC
CENTERS.
DELTA-COMPLETENESS
AND
DELTA-COMPACTNESS
*
16
2.3
ROTUND
METRIC
SPACES
*
18
2.4
OPIAL
CONDITION
AND
VAN
DULST
NORM
*
21
2.5
DEFECT
OF
ENERGY.
BREZIS-LIEB
LEMMA
WITH
DELTA-CONVERGENCE
*
25
2.6
BIBLIOGRAPHIC
NOTES
*
27
3
COCOMPACT
EMBEDDINGS
WITH
THE
RESCALING
GROUP
*
29
3.1
DEFINITIONS
AND
ELEMENTARY
PROPERTIES
OF
COCOMPACTNESS
*
29
3.2
COCOMPACTNESS
OF
THE
LIMITING
SOBOLEV
EMBEDDING
*
30
3.3
EMBEDDING
H
1,P
(1R
N
)
-
L
P
*
*
P
(R
N
)
IS
NOT
COCOMPACT
*
34
3.4
COCOMPACTNESS
AND
EXISTENCE
OF
MINIMIZERS
*
35
3.5
COCOMPACT
EMBEDDINGS
OF
BESOV
AND
TRIEBEL-LIZORKIN
SPACES
*
37
3.6
COCOMPACTNESS
AND
INTERPOLATION
*
40
3.7
COCOMPACT
EMBEDDINGS
OF
INHOMOGENEOUS
BESOV
SPACES
*
44
3.8
COCOMPACT
EMBEDDINGS
OF
INTERSECTIONS
WITH
L
P
(
R
N
)
*
49
3.9
COCOMPACTNESS
OF
TRACE
EMBEDDINGS
*
51
3.10
SPACES
COCOMPACTLY
EMBEDDED
INTO
THEMSELVES
*
54
3.11
COCOMPACTNESS
OF
THE
RADIAL
MOSER-TRUDINGER
EMBEDDING
*
55
3.12
BIBLIOGRAPHIC
NOTES
*
57
4
PROFILE
DECOMPOSITION
IN
BANACH
SPACES
*
59
4.1
PROFILE
DECOMPOSITION
*
59
4.2
OPIAL
CONDITION
IN
BESOV
AND
TRIEBEL-LIZORKIN
SPACES
*
61
4.3
PROOF
OF
THEOREM
4.1.6
-----63
4.4
PROFILE
DECOMPOSITION
IN
THE DUAL
SPACE
*
66
4.5
PROFILE
DECOMPOSITION
FOR
VECTOR-VALUED
FUNCTIONS
*
68
4.6
PROFILE
DECOMPOSITION
IN
BESOV,
TRIEBEL-LIZORKIN,
AND
SOBOLEV
SPACES
*
70
X
*
CONTENTS
4.7
DECOUPLING
OF
NONLINEAR
FUNCTIONALS
*
73
4.8
PROFILE
DECOMPOSITION
FOR
THE
MOSER-TRUDINGER
INEQUALITY
*
78
4.9
BIBLIOGRAPHIC
NOTES
*
79
5
MORE
COCOMPACT
EMBEDDINGS
*
81
5.1
SOBOLEV
SPACES
WITH
PERIODIC
MAGNETIC
FIELD
*
81
5.2
COCOMPACTNESS
OF
SUBELLIPTIC
SOBOLEV
EMBEDDINGS
*
86
5.3
COCOMPACTNESS
OF
A
STRICHARTZ
EMBEDDING
*
91
5.4
AFFINE
SOBOLEV
INEQUALITY
AND
AFFINE
LAPLACIAN
*
96
5.5
BIBLIOGRAPHIC
NOTES
*
99
6
PROFILE
DECOMPOSITIONS
ON
SUBSETS
*
101
6.1
FLASK
SUBSETS,
^-COMPACTNESS
*
101
6.2
PROFILE
DECOMPOSITIONS
FOR
INTERSECTION
OF
TWO
SPACES
*
102
6.3
FLASK
DOMAINS
FOR
SOBOLEV
EMBEDDINGS
*
106
6.4
ASYMPTOTICALLY
NULL
SETS,
COMPACT
SOBOLEV
EMBEDDINGS
*
110
6.5
FLASK
DOMAINS
AND
NULL
SETS
FOR
THE
AFFINE
SOBOLEV
INEQUALITY
*
111
6.6
BIBLIOGRAPHIC
NOTES
*
116
7
GLOBAL
COMPACTNESS
ON
RIEMANNIAN
MANIFOLDS
*
117
7.1
BOUNDED
GEOMETRY.
DISCRETIZATIONS
AND
A
*
SPOTLIGHT
LEMMA
*
*
117
7.2
MANIFOLDS
AT
INFINITY
*
120
7.3
LOCAL
AND
GLOBAL
PROFILES.
PROFILE
DECOMPOSITION
*
125
7.4
AUXILIARY
STATEMENTS
*
127
7.5
PROOF
OF
THEOREM
7.3.5
*
134
7.6
LOCAL
AND
GLOBAL
PROFILE
DECOMPOSITIONS
ON
PERIODIC
MANIFOLDS
*
138
7.7
COCOMPACTNESS
OF
THE
LIMITING
SOBOLEV
EMBEDDING
*
140
7.8
PROFILE
DECOMPOSITION
FOR
SEQUENCES
VANISHING
IN
L
P
,
P
2*
*
142
7.9
PROFILE
DECOMPOSITION
-
THE
LIMITING
CASE
*
150
7.10
COMPACTNESS
IN
PRESENCE
OF
SYMMETRIES
*
152
7.11
BIBLIOGRAPHIC
NOTES
*
156
8
FUNCTIONS
OF
BOUNDED
VARIATION.
SOBOLEV
SPACES
ON
FRACTALS
*
159
8.1
COCOMPACTNESS
OF
THE
EMBEDDING
BV
-
Z.
1
*
(JR
W
)
*
159
8.2
PROFILE
DECOMPOSITION
IN
BV
*
161
8.3
SAMPLE
MINIMIZATION
PROBLEMS
*
163
8.4
FRACTALS
AND
FRACTAL
BLOWUPS
*
165
8.5
SOBOLEV
INEQUALITY
AND
COCOMPACTNESS
ON
FRACTALS
*
167
8.6
MINIMIZERS
ON
FRACTAL
BLOWUPS
*
170
8.7
BIBLIOGRAPHIC
NOTES
*
172
9
SAMPLE
APPLICATIONS
TO
VARIATIONAL
PROBLEMS
*
173
CONTENTS
*
XI
9.1
9.2
9.3
9.4
9.5
NONLINEAR
SCHRODINGER
EQUATION
WITH
POSITIVE
MASS
*
173
NONLINEAR
SCHRODINGER
EQUATION
-
ZERO
MASS
CASE
*
180
EQUATIONS
WITH
FINITE
SYMMETRY
*
182
BLOWUPS
FOR
THE
MOSER-TRUDINGER
FUNCTIONAL
*
183
BIBLIOGRAPHIC
NOTES
*
189
10
10.1
10.2
10.3
10.4
APPENDIX
*
*
191
TOPICS
IN
FUNCTIONAL
ANALYSIS
*
191
FUNCTION
SPACES
WITH
SCALE
INVARIANCE
*
195
MANIFOLDS
OF
BOUNDED
GEOMETRY
*
200
CONCENTRATION
COMPACTNESS
-
TRADITIONAL
APPROACH
*
202
COMMON
NOTATIONS
*
207
BIBLIOGRAPHY-----
209
INDEX
*
215
|
| adam_txt |
CONTENTS
PREFACE
*
VII
1
PROFILE
DECOMPOSITION:
A
STRUCTURED
DEFECT
OF
COMPACTNESS
*
1
1.1
COCOMPACT
EMBEDDINGS:
DEFINITION
AND
EXAMPLES
*
1
1.2
PROFILE
DECOMPOSITION
*
5
1.3
BREZIS-LIEB
LEMMA
*
7
1.4
LIONS
*
LEMMA
FOR
THE
MOSER-TRUDINGER
FUNCTIONAL
*
11
1.5
BIBLIOGRAPHIC
NOTES
*
13
2
DELTA-CONVERGENCE
AND
WEAK
CONVERGENCE
*
15
2.1
DEFINITION
OF
DELTA-CONVERGENCE
*
15
2.2
CHEBYSHEV
AND
ASYMPTOTIC
CENTERS.
DELTA-COMPLETENESS
AND
DELTA-COMPACTNESS
*
16
2.3
ROTUND
METRIC
SPACES
*
18
2.4
OPIAL
CONDITION
AND
VAN
DULST
NORM
*
21
2.5
DEFECT
OF
ENERGY.
BREZIS-LIEB
LEMMA
WITH
DELTA-CONVERGENCE
*
25
2.6
BIBLIOGRAPHIC
NOTES
*
27
3
COCOMPACT
EMBEDDINGS
WITH
THE
RESCALING
GROUP
*
29
3.1
DEFINITIONS
AND
ELEMENTARY
PROPERTIES
OF
COCOMPACTNESS
*
29
3.2
COCOMPACTNESS
OF
THE
LIMITING
SOBOLEV
EMBEDDING
*
30
3.3
EMBEDDING
H
1,P
(1R
N
)
-
L
P
*
*
P
(R
N
)
IS
NOT
COCOMPACT
*
34
3.4
COCOMPACTNESS
AND
EXISTENCE
OF
MINIMIZERS
*
35
3.5
COCOMPACT
EMBEDDINGS
OF
BESOV
AND
TRIEBEL-LIZORKIN
SPACES
*
37
3.6
COCOMPACTNESS
AND
INTERPOLATION
*
40
3.7
COCOMPACT
EMBEDDINGS
OF
INHOMOGENEOUS
BESOV
SPACES
*
44
3.8
COCOMPACT
EMBEDDINGS
OF
INTERSECTIONS
WITH
L
P
(
R
N
)
*
49
3.9
COCOMPACTNESS
OF
TRACE
EMBEDDINGS
*
51
3.10
SPACES
COCOMPACTLY
EMBEDDED
INTO
THEMSELVES
*
54
3.11
COCOMPACTNESS
OF
THE
RADIAL
MOSER-TRUDINGER
EMBEDDING
*
55
3.12
BIBLIOGRAPHIC
NOTES
*
57
4
PROFILE
DECOMPOSITION
IN
BANACH
SPACES
*
59
4.1
PROFILE
DECOMPOSITION
*
59
4.2
OPIAL
CONDITION
IN
BESOV
AND
TRIEBEL-LIZORKIN
SPACES
*
61
4.3
PROOF
OF
THEOREM
4.1.6
-----63
4.4
PROFILE
DECOMPOSITION
IN
THE DUAL
SPACE
*
66
4.5
PROFILE
DECOMPOSITION
FOR
VECTOR-VALUED
FUNCTIONS
*
68
4.6
PROFILE
DECOMPOSITION
IN
BESOV,
TRIEBEL-LIZORKIN,
AND
SOBOLEV
SPACES
*
70
X
*
CONTENTS
4.7
DECOUPLING
OF
NONLINEAR
FUNCTIONALS
*
73
4.8
PROFILE
DECOMPOSITION
FOR
THE
MOSER-TRUDINGER
INEQUALITY
*
78
4.9
BIBLIOGRAPHIC
NOTES
*
79
5
MORE
COCOMPACT
EMBEDDINGS
*
81
5.1
SOBOLEV
SPACES
WITH
PERIODIC
MAGNETIC
FIELD
*
81
5.2
COCOMPACTNESS
OF
SUBELLIPTIC
SOBOLEV
EMBEDDINGS
*
86
5.3
COCOMPACTNESS
OF
A
STRICHARTZ
EMBEDDING
*
91
5.4
AFFINE
SOBOLEV
INEQUALITY
AND
AFFINE
LAPLACIAN
*
96
5.5
BIBLIOGRAPHIC
NOTES
*
99
6
PROFILE
DECOMPOSITIONS
ON
SUBSETS
*
101
6.1
FLASK
SUBSETS,
^-COMPACTNESS
*
101
6.2
PROFILE
DECOMPOSITIONS
FOR
INTERSECTION
OF
TWO
SPACES
*
102
6.3
FLASK
DOMAINS
FOR
SOBOLEV
EMBEDDINGS
*
106
6.4
ASYMPTOTICALLY
NULL
SETS,
COMPACT
SOBOLEV
EMBEDDINGS
*
110
6.5
FLASK
DOMAINS
AND
NULL
SETS
FOR
THE
AFFINE
SOBOLEV
INEQUALITY
*
111
6.6
BIBLIOGRAPHIC
NOTES
*
116
7
GLOBAL
COMPACTNESS
ON
RIEMANNIAN
MANIFOLDS
*
117
7.1
BOUNDED
GEOMETRY.
DISCRETIZATIONS
AND
A
*
SPOTLIGHT
LEMMA
*
*
117
7.2
MANIFOLDS
AT
INFINITY
*
120
7.3
LOCAL
AND
GLOBAL
PROFILES.
PROFILE
DECOMPOSITION
*
125
7.4
AUXILIARY
STATEMENTS
*
127
7.5
PROOF
OF
THEOREM
7.3.5
*
134
7.6
LOCAL
AND
GLOBAL
PROFILE
DECOMPOSITIONS
ON
PERIODIC
MANIFOLDS
*
138
7.7
COCOMPACTNESS
OF
THE
LIMITING
SOBOLEV
EMBEDDING
*
140
7.8
PROFILE
DECOMPOSITION
FOR
SEQUENCES
VANISHING
IN
L
P
,
P
2*
*
142
7.9
PROFILE
DECOMPOSITION
-
THE
LIMITING
CASE
*
150
7.10
COMPACTNESS
IN
PRESENCE
OF
SYMMETRIES
*
152
7.11
BIBLIOGRAPHIC
NOTES
*
156
8
FUNCTIONS
OF
BOUNDED
VARIATION.
SOBOLEV
SPACES
ON
FRACTALS
*
159
8.1
COCOMPACTNESS
OF
THE
EMBEDDING
BV
-
Z.
1
*
(JR
W
)
*
159
8.2
PROFILE
DECOMPOSITION
IN
BV
*
161
8.3
SAMPLE
MINIMIZATION
PROBLEMS
*
163
8.4
FRACTALS
AND
FRACTAL
BLOWUPS
*
165
8.5
SOBOLEV
INEQUALITY
AND
COCOMPACTNESS
ON
FRACTALS
*
167
8.6
MINIMIZERS
ON
FRACTAL
BLOWUPS
*
170
8.7
BIBLIOGRAPHIC
NOTES
*
172
9
SAMPLE
APPLICATIONS
TO
VARIATIONAL
PROBLEMS
*
173
CONTENTS
*
XI
9.1
9.2
9.3
9.4
9.5
NONLINEAR
SCHRODINGER
EQUATION
WITH
POSITIVE
MASS
*
173
NONLINEAR
SCHRODINGER
EQUATION
-
ZERO
MASS
CASE
*
180
EQUATIONS
WITH
FINITE
SYMMETRY
*
182
BLOWUPS
FOR
THE
MOSER-TRUDINGER
FUNCTIONAL
*
183
BIBLIOGRAPHIC
NOTES
*
189
10
10.1
10.2
10.3
10.4
APPENDIX
*
*
191
TOPICS
IN
FUNCTIONAL
ANALYSIS
*
191
FUNCTION
SPACES
WITH
SCALE
INVARIANCE
*
195
MANIFOLDS
OF
BOUNDED
GEOMETRY
*
200
CONCENTRATION
COMPACTNESS
-
TRADITIONAL
APPROACH
*
202
COMMON
NOTATIONS
*
207
BIBLIOGRAPHY-----
209
INDEX
*
215 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Tintarev, Kyril 1956- |
| author_GND | (DE-588)1205670777 |
| author_facet | Tintarev, Kyril 1956- |
| author_role | aut |
| author_sort | Tintarev, Kyril 1956- |
| author_variant | k t kt |
| building | Verbundindex |
| bvnumber | BV046623856 |
| classification_rvk | SK 540 SK 600 |
| ctrlnum | (OCoLC)1124325772 (DE-599)DNB1196888213 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV046623856 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T14:08:46Z |
| indexdate | 2024-07-10T08:49:32Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110530346 3110530341 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032035537 |
| oclc_num | 1124325772 |
| open_access_boolean | |
| owner | DE-20 DE-11 |
| owner_facet | DE-20 DE-11 |
| physical | XI, 216 Seiten 25 cm, 544 g |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter series in nonlinear analysis and applications |
| series2 | De Gruyter series in nonlinear analysis and applications |
| spelling | Tintarev, Kyril 1956- Verfasser (DE-588)1205670777 aut Concentration compactness functional-analytic theory of concentration phenomena Cyril Tintarev Berlin : Boston De Gruyter [2020] XI, 216 Seiten 25 cm, 544 g txt rdacontent n rdamedia nc rdacarrier De Gruyter series in nonlinear analysis and applications volume 33 Kompaktheit (DE-588)4456100-3 gnd rswk-swf Konvergenz (DE-588)4032326-2 gnd rswk-swf Einbettung Mathematik (DE-588)4151233-9 gnd rswk-swf Folge Mathematik (DE-588)4017790-7 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Funktionalanalysis Kompaktheit Nichtlineare elliptische Differentialgleichung Nichtlineare Funktionalanalysis Schwache Konvergenz Banach-Raum (DE-588)4004402-6 s Folge Mathematik (DE-588)4017790-7 s Konvergenz (DE-588)4032326-2 s Kompaktheit (DE-588)4456100-3 s Einbettung Mathematik (DE-588)4151233-9 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe 9783110532432 Erscheint auch als Online-Ausgabe, PDF 978-3-11-053243-2 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-053058-2 De Gruyter series in nonlinear analysis and applications volume 33 (DE-604)BV005530011 33 B:DE-101 application/pdf https://d-nb.info/1196888213/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032035537&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tintarev, Kyril 1956- Concentration compactness functional-analytic theory of concentration phenomena De Gruyter series in nonlinear analysis and applications Kompaktheit (DE-588)4456100-3 gnd Konvergenz (DE-588)4032326-2 gnd Einbettung Mathematik (DE-588)4151233-9 gnd Folge Mathematik (DE-588)4017790-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4456100-3 (DE-588)4032326-2 (DE-588)4151233-9 (DE-588)4017790-7 (DE-588)4004402-6 |
| title | Concentration compactness functional-analytic theory of concentration phenomena |
| title_auth | Concentration compactness functional-analytic theory of concentration phenomena |
| title_exact_search | Concentration compactness functional-analytic theory of concentration phenomena |
| title_exact_search_txtP | Concentration compactness functional-analytic theory of concentration phenomena |
| title_full | Concentration compactness functional-analytic theory of concentration phenomena Cyril Tintarev |
| title_fullStr | Concentration compactness functional-analytic theory of concentration phenomena Cyril Tintarev |
| title_full_unstemmed | Concentration compactness functional-analytic theory of concentration phenomena Cyril Tintarev |
| title_short | Concentration compactness |
| title_sort | concentration compactness functional analytic theory of concentration phenomena |
| title_sub | functional-analytic theory of concentration phenomena |
| topic | Kompaktheit (DE-588)4456100-3 gnd Konvergenz (DE-588)4032326-2 gnd Einbettung Mathematik (DE-588)4151233-9 gnd Folge Mathematik (DE-588)4017790-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Kompaktheit Konvergenz Einbettung Mathematik Folge Mathematik Banach-Raum |
| url | https://d-nb.info/1196888213/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032035537&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT tintarevkyril concentrationcompactnessfunctionalanalytictheoryofconcentrationphenomena AT walterdegruytergmbhcokg concentrationcompactnessfunctionalanalytictheoryofconcentrationphenomena |
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