Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2006
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
857 = 182,1 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014861487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | "Volume 182, number 857 (first of 4 numbers)." Includes bibliographical references |
| Umfang: | IX, 119 S. |
| ISBN: | 082183911X |
Internformat
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| 245 | 1 | 0 | |a Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces |c Donatella Danielli ; Nicola Garofalo ; Duy-Minh Nhieu |
| 246 | 1 | 0 | |a Non doubling Ahlfors measures, perimeter measures, and the charcterization of the trace spaces of Soboloev functions in Carnot-Carathéodory spaces |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2006 | |
| 300 | |a IX, 119 S. | ||
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| 650 | 7 | |a Harmonische analyse |2 gtt | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 4 | |a Homogeneous spaces | |
| 650 | 4 | |a Sobolev spaces | |
| 650 | 4 | |a Measure theory | |
| 650 | 4 | |a Differential equations, Partial | |
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Datensatz im Suchindex
| _version_ | 1819354711310991360 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
1.1. Carnot Caratheodory spaces 9
1.2. The Chow Rashevsky s accessibility theorem and CC metrics 9
1.3. The Nagel Stein Wainger polynomial and the size of the CC balls 11
Chapter 2. Carnot groups 15
2.1. Carnot groups of step 2 17
2.2. The Kaplan mapping 19
2.3. Groups of Heisenberg type 20
Chapter 3. The characteristic set 23
3.1. A result of Derridj on the size of the characteristic set 23
3.2. Some geometric examples 24
3.3. Non characteristic manifolds 24
3.4. Manifolds with controlled characteristic set 27
Chapter 4. X variation, X perimeter and surface measure 33
4.1. The structure of functions in BVx,ioc 33
4.2. X Caccioppoli sets 34
4.3. X perimeter and the perimeter measure 36
Chapter 5. Geometric estimates from above on CC balls for the
perimeter measure 37
5.1. A fundamental estimate 37
5.2. The X perimeter of a C1 1 domain is an upper 1 Ahlfors measure 39
Chapter 6. Geometric estimates from below on CC balls for the
perimeter measure 41
6.1. The relative isoperimetric inequality and Theorem 6.1 42
6.2. A basic geometric lemma 43
6.3. Further analysis for Hormander vector fields of step 2 46
6.4. Second proof of Theorem 6.1 52
6.5. Failure of the 1 Ahlfors condition for the X perimeter of Cla domains 55
Chapter 7. Fine differentiability properties of Sobolev functions 57
7.1. Poincare inequality, fractional integrals and improved representation
formulas 57
7.2. Fine mapping properties of fractional integration on metric spaces 61
7.3. Differentiation with respect to an upper Ahlfors measure 62
7.4. Upper Ahlfors measures and Hausdorff measure 63
vii
viii CONTENTS
Chapter 8. Embedding a Sobolev space into a Besov space with
respect to an upper Ahlfors measure 65
8.1. Some results from harmonic analysis 65
8.2. Two simple growth estimates 66
8.3. A key continuity estimate for a singular integral 67
8.4. The main theorem 69
Chapter 9. The extension theorem for a Besov space with respect to
a lower Ahlfors measure 79
9.1. Some auxiliary results 79
9.2. Proof of Theorem 9.1 80
Chapter 10. Traces on the boundary of (e, S) domains 85
10.1. The (e, S) condition is optimal for the existence of traces 88
10.2. Characterization of the traces on the boundary 90
Chapter 11. The embedding of B^(n,d/j,) into Lq{Q.,dn) 93
Chapter 12. Returning to Carnot groups 99
Chapter 13. The Neumann problem 103
Chapter 14. The case of Lipschitz vector fields 109
Bibliography 111
|
| any_adam_object | 1 |
| author | Danielli, Donatella 1966- Garofalo, Nicola Nhieu, Duy-Minh 1966- |
| author_GND | (DE-588)131806041 (DE-588)1295607778 (DE-588)131809873 |
| author_facet | Danielli, Donatella 1966- Garofalo, Nicola Nhieu, Duy-Minh 1966- |
| author_role | aut aut aut |
| author_sort | Danielli, Donatella 1966- |
| author_variant | d d dd n g ng d m n dmn |
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| classification_rvk | SI 130 |
| ctrlnum | (OCoLC)65644672 (DE-599)BVBBV021646787 |
| dewey-full | 515/.2433 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515/.2433 510 |
| dewey-search | 515/.2433 510 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV021646787 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T12:38:29Z |
| institution | BVB |
| isbn | 082183911X |
| language | English |
| lccn | 2006042821 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014861487 |
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| physical | IX, 119 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spellingShingle | Danielli, Donatella 1966- Garofalo, Nicola Nhieu, Duy-Minh 1966- Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces Memoirs of the American Mathematical Society Geometria diferencial (textos avançados) larpcal Harmonische analyse gtt Harmonic analysis Homogeneous spaces Sobolev spaces Measure theory Differential equations, Partial Maßtheorie (DE-588)4074626-4 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4055345-0 |
| title | Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces |
| title_alt | Non doubling Ahlfors measures, perimeter measures, and the charcterization of the trace spaces of Soboloev functions in Carnot-Carathéodory spaces |
| title_auth | Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces |
| title_exact_search | Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces |
| title_full | Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces Donatella Danielli ; Nicola Garofalo ; Duy-Minh Nhieu |
| title_fullStr | Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces Donatella Danielli ; Nicola Garofalo ; Duy-Minh Nhieu |
| title_full_unstemmed | Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces Donatella Danielli ; Nicola Garofalo ; Duy-Minh Nhieu |
| title_short | Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces |
| title_sort | non doubling ahlfors measures perimeter measures and the characterization of the trace spaces of sobolev functions in carnot caratheodory spaces |
| topic | Geometria diferencial (textos avançados) larpcal Harmonische analyse gtt Harmonic analysis Homogeneous spaces Sobolev spaces Measure theory Differential equations, Partial Maßtheorie (DE-588)4074626-4 gnd Sobolev-Raum (DE-588)4055345-0 gnd |
| topic_facet | Geometria diferencial (textos avançados) Harmonische analyse Harmonic analysis Homogeneous spaces Sobolev spaces Measure theory Differential equations, Partial Maßtheorie Sobolev-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014861487&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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