Nonlinear potential theory and weighted Sobolev spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2000
|
| Series: | Lecture notes in mathematics
1736 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 173 S. |
| ISBN: | 3540675884 |
Staff View
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| 245 | 1 | 0 | |a Nonlinear potential theory and weighted Sobolev spaces |c Bengt Ove Turesson |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction v
1. Preliminaries 1
1.1. Notation and conventions 1
1.2. Basic results concerning weights 2
1.2.1. General weights 2
1.2.2. Ap weights 3
1.2.3. Doubling weights 6
1.2.4. Aoo weights 7
1.2.5. Proof of Muckenhoupt s maximal theorem 10
1.2.6. Boundedness of singular integrals 12
1.2.7. Two theorems by Muckenhoupt and Wheeden 12
2. Sobolev spaces 15
2.1. The Sobolev space Wâ„¢ P(fi) 16
2.1.1. Approximation results 17
2.1.2. Extension theorems 19
2.1.3. An interpolation inequality 23
2.2. The Sobolev space Vâ„¢ P(U) 25
2.3. Hausdorff measures 37
2.4. Isoperimetric inequalities 40
2.4.1. Preliminary lemmas 41
2.4.2. Extensions of some results by David and Semmes 44
2.4.3. Isoperimetric inequalities involving lower Minkowski content 47
2.4.4. Isoperimetric inequalities with Hausdorff measures .... 49
2.4.5. A boxing inequality 53
2.5. Some Sobolev type inequalities 54
2.6. Embeddings into L«(fi) 58
2.6.1. Introduction 59
2.6.2. Embedding theorems 62
xiv Contents
3. Potential theory 69
3.1. Norm inequalities for fractional integrals and maximal functions 70
3.1.1. Proof of the main inequality and some corollaries 70
3.1.2. An inequality for Bessel potentials 75
3.2. Meyers theory for Incapacities 77
3.2.1. Outline of Meyers theory 77
3.2.2. Capacitary measures and capacitary potentials 80
3.3. Bessel and Riesz capacities 88
3.3.1. Basic properties 88
3.3.2. Adams formula for the capacity of a ball 92
3.4. Hausdorff capacities 97
3.4.1. Basic properties 97
3.4.2. The capacity of a ball 99
3.4.3. Non triviality of U^ 104
3.4.4. Local equivalence between U% a and n%£? 108
3.4.5. Continuity properties 110
3.4.6. Frostman s lemma 113
3.5. Variational capacities 115
3.5.1. The case 1 p oo 115
3.5.2. The casep= 1 117
3.5.3. An embedding theorem 120
3.6. Thinness: The case 1 p oo 121
3.6.1. Preliminary considerations 122
3.6.2. A Wolff type inequality 124
3.6.3. Proof of the Kellogg property 127
3.6.4. A concept of thinness based on a condensor capacity . . . 131
3.7. Thinness: The case p = 1 134
4. Applications of potential theory to Sobolev spaces 141
4.1. Quasicontinuity 141
4.1.1. The case 1 p oo 142
4.1.2. The case p = 1 144
4.2. Measures in the dual of Wâ„¢lP(n) 148
4.2.1. The case 1 p oo 148
4.2.2. The case p = 1 149
4.3. Poincare type inequalities 151
4.3.1. The case 1 p oo 151
4.3.2. The case p = 1 155
4.4. Spectral synthesis 156
4.4.1. The case 1 p oo 157
4.4.2. The case p = 1 160
References 163
Index 171
|
| any_adam_object | 1 |
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| dewey-ones | 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:39:57Z |
| institution | BVB |
| isbn | 3540675884 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008961996 |
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| physical | XIV, 173 S. |
| publishDate | 2000 |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Turesson, Bengt Ove Verfasser aut Nonlinear potential theory and weighted Sobolev spaces Bengt Ove Turesson Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2000 XIV, 173 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1736 Nichtlineare Potenzialtheorie - Gewichteter Sobolev-Raum Nonlinear theories Potential theory (Mathematics) Sobolev spaces Nichtlineare Potenzialtheorie (DE-588)4315456-6 gnd rswk-swf Gewichteter Sobolev-Raum (DE-588)4194344-2 gnd rswk-swf Nichtlineare Potenzialtheorie (DE-588)4315456-6 s Gewichteter Sobolev-Raum (DE-588)4194344-2 s DE-604 Lecture notes in mathematics 1736 (DE-604)BV000676446 1736 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008961996&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Turesson, Bengt Ove Nonlinear potential theory and weighted Sobolev spaces Lecture notes in mathematics Nichtlineare Potenzialtheorie - Gewichteter Sobolev-Raum Nonlinear theories Potential theory (Mathematics) Sobolev spaces Nichtlineare Potenzialtheorie (DE-588)4315456-6 gnd Gewichteter Sobolev-Raum (DE-588)4194344-2 gnd |
| subject_GND | (DE-588)4315456-6 (DE-588)4194344-2 |
| title | Nonlinear potential theory and weighted Sobolev spaces |
| title_auth | Nonlinear potential theory and weighted Sobolev spaces |
| title_exact_search | Nonlinear potential theory and weighted Sobolev spaces |
| title_full | Nonlinear potential theory and weighted Sobolev spaces Bengt Ove Turesson |
| title_fullStr | Nonlinear potential theory and weighted Sobolev spaces Bengt Ove Turesson |
| title_full_unstemmed | Nonlinear potential theory and weighted Sobolev spaces Bengt Ove Turesson |
| title_short | Nonlinear potential theory and weighted Sobolev spaces |
| title_sort | nonlinear potential theory and weighted sobolev spaces |
| topic | Nichtlineare Potenzialtheorie - Gewichteter Sobolev-Raum Nonlinear theories Potential theory (Mathematics) Sobolev spaces Nichtlineare Potenzialtheorie (DE-588)4315456-6 gnd Gewichteter Sobolev-Raum (DE-588)4194344-2 gnd |
| topic_facet | Nichtlineare Potenzialtheorie - Gewichteter Sobolev-Raum Nonlinear theories Potential theory (Mathematics) Sobolev spaces Nichtlineare Potenzialtheorie Gewichteter Sobolev-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008961996&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT turessonbengtove nonlinearpotentialtheoryandweightedsobolevspaces |