Hölder continuity of weak solutions to subelliptic equations with rough coefficients:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2006
|
| Series: | Memoirs of the American Mathematical Society
847 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references |
| Physical Description: | IX, 157 S. |
| ISBN: | 0821838261 |
Staff View
MARC
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| 100 | 1 | |a Sawyer, Eric T. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hölder continuity of weak solutions to subelliptic equations with rough coefficients |c Eric T. Sawyer ; Richard L. Wheeden |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2006 | |
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Record in the Search Index
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| adam_text | Contents
Overview ix
Chapter 1. Introduction 1
1. An extension of the Fefferman-Phong theorem to rough operators 6
2. Extensions of Hormander s theorem to rough operators 15
3. Applications to quasilinear equations 24
Chapter 2. Comparisons of conditions 29
1. Flags and commutators 29
2. Homogeneous and prehomogeneous spaces 31
3. Comparability with the subunit balls 42
Chapter 3. Proof of the general subellipticity theorem 53
1. W-weak solutions and admissible compositions 55
2. Weak reverse Holder inequalities and Moser iteration 66
3. The strong Harnack inequality 74
4. Holder continuity of solutions 84
Chapter 4. Reduction of the proofs of the rough diagonal extensions of
Hormander s theorem 87
1. Accumulating sequences of Lipschitz cutoff functions in annuli 87
2. The axiom 91
3. The Sobolev and Poincare inequalities 94
4. Adapted vector fields and prehomogeneous spaces 97
5. The reduction of the proofs 111
Chapter 5. Homogeneous spaces and subrepresentation inequalities 117
1. The noninterference balls 117
2. The flag balls 119
Chapter 6. Appendix 133
1. Necessity of the Fefferman-Phong condition 133
2. Necessity of the Sobolev and Poincare inequalities 136
3. The noninterference balls A (x, r) and the reverse Holder condition 138
4. Reverse Holder examples 140
V
vi CONTENTS
5. Product reverse Holder 143
6. The noninterference conditions 147
7. Other notions of weak solution 150
8. Alternate methods of proof 151
Bibliography 153
Glossary of Terms and Symbols 155
|
| adam_txt |
Contents
Overview ix
Chapter 1. Introduction 1
1. An extension of the Fefferman-Phong theorem to rough operators 6
2. Extensions of Hormander's theorem to rough operators 15
3. Applications to quasilinear equations 24
Chapter 2. Comparisons of conditions 29
1. Flags and commutators 29
2. Homogeneous and prehomogeneous spaces 31
3. Comparability with the subunit balls 42
Chapter 3. Proof of the general subellipticity theorem 53
1. W-weak solutions and admissible compositions 55
2. Weak reverse Holder inequalities and Moser iteration 66
3. The strong Harnack inequality 74
4. Holder continuity of solutions 84
Chapter 4. Reduction of the proofs of the rough diagonal extensions of
Hormander's theorem 87
1. Accumulating sequences of Lipschitz cutoff functions in annuli 87
2. The axiom 91
3. The Sobolev and Poincare inequalities 94
4. Adapted vector fields and prehomogeneous spaces 97
5. The reduction of the proofs 111
Chapter 5. Homogeneous spaces and subrepresentation inequalities 117
1. The noninterference balls 117
2. The flag balls 119
Chapter 6. Appendix 133
1. Necessity of the Fefferman-Phong condition 133
2. Necessity of the Sobolev and Poincare inequalities 136
3. The noninterference balls A (x, r) and the reverse Holder condition 138
4. Reverse Holder examples 140
V
vi CONTENTS
5. Product reverse Holder 143
6. The noninterference conditions 147
7. Other notions of weak solution 150
8. Alternate methods of proof 151
Bibliography 153
Glossary of Terms and Symbols 155 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T14:30:05Z |
| indexdate | 2024-07-09T20:38:19Z |
| institution | BVB |
| isbn | 0821838261 |
| language | English |
| lccn | 2005057158 |
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| physical | IX, 157 S. |
| publishDate | 2006 |
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| publisher | American Mathematical Society |
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| series2 | Memoirs of the American Mathematical Society |
| spelling | Sawyer, Eric T. Verfasser aut Hölder continuity of weak solutions to subelliptic equations with rough coefficients Eric T. Sawyer ; Richard L. Wheeden Providence, RI American Mathematical Society 2006 IX, 157 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 847 Includes bibliographical references Equações diferenciais parciais eliticas (análise) larpcal Partiële differentiaalvergelijkingen gtt Differential equations, Partial Numerical solutions Differential equations, Hypoelliptic Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Komplexe Differentialgleichung (DE-588)4161117-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Komplexe Differentialgleichung (DE-588)4161117-2 s b DE-604 Wheeden, Richard L. Verfasser aut Memoirs of the American Mathematical Society 847 (DE-604)BV008000141 847 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014762917&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sawyer, Eric T. Wheeden, Richard L. Hölder continuity of weak solutions to subelliptic equations with rough coefficients Memoirs of the American Mathematical Society Equações diferenciais parciais eliticas (análise) larpcal Partiële differentiaalvergelijkingen gtt Differential equations, Partial Numerical solutions Differential equations, Hypoelliptic Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Komplexe Differentialgleichung (DE-588)4161117-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4161117-2 (DE-588)4044779-0 |
| title | Hölder continuity of weak solutions to subelliptic equations with rough coefficients |
| title_auth | Hölder continuity of weak solutions to subelliptic equations with rough coefficients |
| title_exact_search | Hölder continuity of weak solutions to subelliptic equations with rough coefficients |
| title_exact_search_txtP | Hölder continuity of weak solutions to subelliptic equations with rough coefficients |
| title_full | Hölder continuity of weak solutions to subelliptic equations with rough coefficients Eric T. Sawyer ; Richard L. Wheeden |
| title_fullStr | Hölder continuity of weak solutions to subelliptic equations with rough coefficients Eric T. Sawyer ; Richard L. Wheeden |
| title_full_unstemmed | Hölder continuity of weak solutions to subelliptic equations with rough coefficients Eric T. Sawyer ; Richard L. Wheeden |
| title_short | Hölder continuity of weak solutions to subelliptic equations with rough coefficients |
| title_sort | holder continuity of weak solutions to subelliptic equations with rough coefficients |
| topic | Equações diferenciais parciais eliticas (análise) larpcal Partiële differentiaalvergelijkingen gtt Differential equations, Partial Numerical solutions Differential equations, Hypoelliptic Numerical solutions Numerisches Verfahren (DE-588)4128130-5 gnd Komplexe Differentialgleichung (DE-588)4161117-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Equações diferenciais parciais eliticas (análise) Partiële differentiaalvergelijkingen Differential equations, Partial Numerical solutions Differential equations, Hypoelliptic Numerical solutions Numerisches Verfahren Komplexe Differentialgleichung Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014762917&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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