Nonlinear analysis on manifolds: Sobolev spaces and inequalities
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Courant Inst. of Math. Sciences
2000
Providence, RI American Math. Soc. |
| Ausgabe: | Repr. |
| Schriftenreihe: | Courant lecture notes in mathematics
5 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 290 S. |
| ISBN: | 0821827006 9780821827000 |
Internformat
MARC
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| 100 | 1 | |a Hebey, Emmanuel |d 1964- |e Verfasser |0 (DE-588)173028551 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear analysis on manifolds |b Sobolev spaces and inequalities |c Emmanuel Hebey |
| 250 | |a Repr. | ||
| 264 | 1 | |a New York, NY |b Courant Inst. of Math. Sciences |c 2000 | |
| 264 | 1 | |a Providence, RI |b American Math. Soc. | |
| 300 | |a XII, 290 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Courant lecture notes in mathematics |v 5 | |
| 650 | 4 | |a Inégalités (Mathématiques) | |
| 650 | 4 | |a Riemann, Variétés de | |
| 650 | 4 | |a Sobolev, Espaces de | |
| 650 | 4 | |a Inequalities (Mathematics) | |
| 650 | 4 | |a Riemannian manifolds | |
| 650 | 4 | |a Sobolev spaces | |
| 650 | 0 | 7 | |a Nichtlineare Analysis |0 (DE-588)4177490-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Riemannscher Raum |0 (DE-588)4128295-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ungleichung |0 (DE-588)4139098-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Sobolev-Raum |0 (DE-588)4055345-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Sobolev-Raum |0 (DE-588)4055345-0 |D s |
| 689 | 0 | 2 | |a Ungleichung |0 (DE-588)4139098-2 |D s |
| 689 | 0 | 3 | |a Riemannscher Raum |0 (DE-588)4128295-4 |D s |
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| 830 | 0 | |a Courant lecture notes in mathematics |v 5 |w (DE-604)BV012714106 |9 5 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009135122 | ||
Datensatz im Suchindex
| _version_ | 1804128173012549632 |
|---|---|
| adam_text | Contents
Preface
xi
Chapter
1.
Elements of Riemannian Geometry
1
1.1.
Smooth Manifolds
1
1.2.
Riemannian Manifolds
7
1.3.
Curvature and Topology
10
1.4.
From Local to Global Analysis
11
1.5.
Special Coordinates
13
Chapter
2.
Sobolev Spaces: The Compact Setting
19
2.1.
Background Material
19
2.2.
Sobolev Spaces on Riemannian Manifolds
21
2.3.
Sobolev Embeddings: General Results
25
2.4.
The Case of the Euclidean Space
30
2.5.
Sobolev Embeddings I
32
2.6.
Sobolev Embeddings II
33
2.7.
Compact Embeddings
37
2.8.
Poincaré
and
Sobolev-Poincaré
Inequalities
40
2.9.
A Finiteness Theorem
44
Chapter
3.
Sobolev Spaces: The Noncompact Setting
47
3.1.
Density Problems
47
3.2.
Sobolev Embeddings I
52
3.3.
Sobolev Embeddings II
63
3.4.
Disturbed Sobolev Inequalities
67
Chapter
4.
Best Constants in the Compact Setting I
75
4.1.
Program
33,
Part I
76
4.2.
The Role of aq(M)
84
4.3.
Program
Л,
Part I
91
4.4.
On the Scale of Optimal Inequalities
114
Chapter
5.
Best Constants in the Compact Setting II
119
5.1.
The Case of the Standard Unit Sphere
120
5.2.
Program
£,
Part II
124
5.3.
Program
Л,
Part
Π
132
5.4.
The Role of
Sote)
150
5.5.
One More Question
155
χ
CONTENTS
Chapter
6.
Optimal Inequalities with Constraints
161
6.1.
The Case of an Arbitrary Compact Manifold
161
6.2.
The Case of the Sphere
166
6.3.
Applications to the Nirenberg Problem
170
Chapter?. Best Constants in the Noncompact Setting
181
7.1.
Questions
1
and
2 182
7.2.
Questions
3
and
4 186
7.3.
Proof of Theorem
7.2 191
7.4.
Explicit Inequalities
222
Chapter
8.
Euclidean-Type Sobolev Inequalities
225
8.1.
Euclidean-Type Generic Sobolev Inequalities
226
8.2.
Euclidean-Type Optimal Sobolev Inequalities
235
8.3.
Nash s Inequality
244
Chapter
9.
The Influence of Symmetries
249
9.1.
Geometric Preliminaries
249
9.2.
Compact Manifolds
251
9.3.
Optimal Inequalities for Compact Manifolds
253
9.4.
Compactness for Radially Symmetric Functions
260
9.5.
A Main Lemma for Complete Manifolds
263
9.6.
The Codimension
1
Case
266
9.7.
The General Case
. 271
Chapter
10.
Manifolds with Boundary
279
Bibliography
283
|
| any_adam_object | 1 |
| author | Hebey, Emmanuel 1964- |
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| author_facet | Hebey, Emmanuel 1964- |
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| ctrlnum | (OCoLC)44727696 (DE-599)BVBBV013391505 |
| 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 3782 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Repr. |
| format | Book |
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| id | DE-604.BV013391505 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:45:02Z |
| institution | BVB |
| isbn | 0821827006 9780821827000 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009135122 |
| oclc_num | 44727696 |
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| physical | XII, 290 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Courant Inst. of Math. Sciences American Math. Soc. |
| record_format | marc |
| series | Courant lecture notes in mathematics |
| series2 | Courant lecture notes in mathematics |
| spelling | Hebey, Emmanuel 1964- Verfasser (DE-588)173028551 aut Nonlinear analysis on manifolds Sobolev spaces and inequalities Emmanuel Hebey Repr. New York, NY Courant Inst. of Math. Sciences 2000 Providence, RI American Math. Soc. XII, 290 S. txt rdacontent n rdamedia nc rdacarrier Courant lecture notes in mathematics 5 Inégalités (Mathématiques) Riemann, Variétés de Sobolev, Espaces de Inequalities (Mathematics) Riemannian manifolds Sobolev spaces Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Ungleichung (DE-588)4139098-2 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 s Sobolev-Raum (DE-588)4055345-0 s Ungleichung (DE-588)4139098-2 s Riemannscher Raum (DE-588)4128295-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1759-8 Courant lecture notes in mathematics 5 (DE-604)BV012714106 5 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009135122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hebey, Emmanuel 1964- Nonlinear analysis on manifolds Sobolev spaces and inequalities Courant lecture notes in mathematics Inégalités (Mathématiques) Riemann, Variétés de Sobolev, Espaces de Inequalities (Mathematics) Riemannian manifolds Sobolev spaces Nichtlineare Analysis (DE-588)4177490-5 gnd Riemannscher Raum (DE-588)4128295-4 gnd Ungleichung (DE-588)4139098-2 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4177490-5 (DE-588)4128295-4 (DE-588)4139098-2 (DE-588)4055345-0 |
| title | Nonlinear analysis on manifolds Sobolev spaces and inequalities |
| title_auth | Nonlinear analysis on manifolds Sobolev spaces and inequalities |
| title_exact_search | Nonlinear analysis on manifolds Sobolev spaces and inequalities |
| title_full | Nonlinear analysis on manifolds Sobolev spaces and inequalities Emmanuel Hebey |
| title_fullStr | Nonlinear analysis on manifolds Sobolev spaces and inequalities Emmanuel Hebey |
| title_full_unstemmed | Nonlinear analysis on manifolds Sobolev spaces and inequalities Emmanuel Hebey |
| title_short | Nonlinear analysis on manifolds |
| title_sort | nonlinear analysis on manifolds sobolev spaces and inequalities |
| title_sub | Sobolev spaces and inequalities |
| topic | Inégalités (Mathématiques) Riemann, Variétés de Sobolev, Espaces de Inequalities (Mathematics) Riemannian manifolds Sobolev spaces Nichtlineare Analysis (DE-588)4177490-5 gnd Riemannscher Raum (DE-588)4128295-4 gnd Ungleichung (DE-588)4139098-2 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Inégalités (Mathématiques) Riemann, Variétés de Sobolev, Espaces de Inequalities (Mathematics) Riemannian manifolds Sobolev spaces Nichtlineare Analysis Riemannscher Raum Ungleichung Sobolev-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009135122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012714106 |
| work_keys_str_mv | AT hebeyemmanuel nonlinearanalysisonmanifoldssobolevspacesandinequalities |