Weakly differentiable mappings between manifolds:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2008
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
899 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "Volume 192, number 899 (fourth of 5 numbers)" Includes bibliographical references |
| Beschreibung: | VII, 72 S. |
| ISBN: | 9780821840795 |
Internformat
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| 245 | 1 | 0 | |a Weakly differentiable mappings between manifolds |c Piotr Hajłasz ... [et al.] |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2008 | |
| 300 | |a VII, 72 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 899 | |
| 500 | |a "Volume 192, number 899 (fourth of 5 numbers)" | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 4 | |a Differentiable manifolds | |
| 650 | 4 | |a Sobolev spaces | |
| 650 | 0 | 7 | |a Differenzierbare Mannigfaltigkeit |0 (DE-588)4012269-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Sobolev-Raum |0 (DE-588)4055345-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differenzierbare Mannigfaltigkeit |0 (DE-588)4012269-4 |D s |
| 689 | 0 | 1 | |a Sobolev-Raum |0 (DE-588)4055345-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Hajłasz, Piotr |e Sonstige |4 oth | |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v 899 |w (DE-604)BV008000141 |9 899 | |
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Datensatz im Suchindex
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| adam_text | Contents
Chapter 1. Introduction 1
Chapter 2. Preliminaries Concerning Manifolds 7
2.1. Manifolds 7
2.2. The Sobolev space Tlj (X, Y) 8
2.3. Differential forms 9
2.4. Mollifiers and smoothing operator 15
2.5. Maximal operators 16
Chapter 3. Examples 21
3.1. The longitude projection 21
3.2. Spherical coordinates 22
3.3. Winding around the longitude circles 22
3.4. A mapping of infinite degree 23
Chapter 4. Some Classes of Functions 25
4.1. Marcinkiewicz space Jzf^oak(X) 25
4.2. The space Jzfa-p(X) 26
4.3. The Orlicz space ifp(X) 28
4.4. Grand Gif -space 31
4.5. Relations between spaces 32
4.6. Sobolev classes 35
Chapter 5. Smooth Approximation 37
5.1. Web like structures 37
5.2. Vanishing web oscillations 37
5.3. Statements of the results 38
5.4. Proof of Theorem 5.1 39
5.5. Spinning a web on X 42
5.6. Proof of Theorems 1.1 and 1.2 44
5.7. Proof of Theorem 5.2 45
5.8. Proof of Theorem 1.3 45
Chapter 6. JSf ^Estimates of the Jacobian 47
6.1. Weak wedge products 48
6.2. Distributional Jacobian 49
6.3. Proof of Theorem 6.5 51
Chapter 7. .if •-Estimates 55
7.1. The Hausdorff content 55
7.2. The ,W^Theorem r 6
Chapter 8. Degree Theory 63
V
vi CONTENTS
8.1. Definition of the degree via weak integrals 63
8.2. Weak integrals 64
8.3. Stability of the degree 66
8.4. The degree in Orlicz and grand Sobolev spaces 67
Chapter 9. Mappings of Finite Distortion 69
Acknowledgements 70
Bibliography 71
|
| adam_txt |
Contents
Chapter 1. Introduction 1
Chapter 2. Preliminaries Concerning Manifolds 7
2.1. Manifolds 7
2.2. The Sobolev space Tlj'(X, Y) 8
2.3. Differential forms 9
2.4. Mollifiers and smoothing operator 15
2.5. Maximal operators 16
Chapter 3. Examples 21
3.1. The longitude projection 21
3.2. Spherical coordinates 22
3.3. Winding around the longitude circles 22
3.4. A mapping of infinite degree 23
Chapter 4. Some Classes of Functions 25
4.1. Marcinkiewicz space Jzf^oak(X) 25
4.2. The space Jzfa-p(X) " 26
4.3. The Orlicz space ifp(X) 28
4.4. Grand Gif"-space 31
4.5. Relations between spaces 32
4.6. Sobolev classes 35
Chapter 5. Smooth Approximation 37
5.1. Web like structures 37
5.2. Vanishing web oscillations 37
5.3. Statements of the results 38
5.4. Proof of Theorem 5.1 39
5.5. Spinning a web on X 42
5.6. Proof of Theorems 1.1 and 1.2 44
5.7. Proof of Theorem 5.2 45
5.8. Proof of Theorem 1.3 45
Chapter 6. JSf ^Estimates of the Jacobian 47
6.1. Weak wedge products 48
6.2. Distributional Jacobian 49
6.3. Proof of Theorem 6.5 51
Chapter 7. .if'•-Estimates 55
7.1. The Hausdorff content 55
7.2. The ,W^Theorem r'6
Chapter 8. Degree Theory 63
V
vi CONTENTS
8.1. Definition of the degree via weak integrals 63
8.2. Weak integrals 64
8.3. Stability of the degree 66
8.4. The degree in Orlicz and grand Sobolev spaces 67
Chapter 9. Mappings of Finite Distortion 69
Acknowledgements 70
Bibliography 71 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:13:27Z |
| indexdate | 2024-07-09T21:13:15Z |
| institution | BVB |
| isbn | 9780821840795 |
| language | English |
| lccn | 2007060584 |
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| physical | VII, 72 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Weakly differentiable mappings between manifolds Piotr Hajłasz ... [et al.] Providence, RI American Mathematical Society 2008 VII, 72 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 899 "Volume 192, number 899 (fourth of 5 numbers)" Includes bibliographical references Differentiable manifolds Sobolev spaces Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Sobolev-Raum (DE-588)4055345-0 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s Sobolev-Raum (DE-588)4055345-0 s DE-604 Hajłasz, Piotr Sonstige oth Memoirs of the American Mathematical Society 899 (DE-604)BV008000141 899 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016400569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weakly differentiable mappings between manifolds Memoirs of the American Mathematical Society Differentiable manifolds Sobolev spaces Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4012269-4 (DE-588)4055345-0 |
| title | Weakly differentiable mappings between manifolds |
| title_auth | Weakly differentiable mappings between manifolds |
| title_exact_search | Weakly differentiable mappings between manifolds |
| title_exact_search_txtP | Weakly differentiable mappings between manifolds |
| title_full | Weakly differentiable mappings between manifolds Piotr Hajłasz ... [et al.] |
| title_fullStr | Weakly differentiable mappings between manifolds Piotr Hajłasz ... [et al.] |
| title_full_unstemmed | Weakly differentiable mappings between manifolds Piotr Hajłasz ... [et al.] |
| title_short | Weakly differentiable mappings between manifolds |
| title_sort | weakly differentiable mappings between manifolds |
| topic | Differentiable manifolds Sobolev spaces Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Differentiable manifolds Sobolev spaces Differenzierbare Mannigfaltigkeit Sobolev-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016400569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT hajłaszpiotr weaklydifferentiablemappingsbetweenmanifolds |