Second order elliptic equations and elliptic systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Chinese |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
1998
|
| Schriftenreihe: | Translations of mathematical monographs
174 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Chines. übers. |
| Beschreibung: | XIII, 246 S. |
| ISBN: | 0821809709 |
Internformat
MARC
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| 245 | 1 | 0 | |a Second order elliptic equations and elliptic systems |c Ya-Zhe Chen ; Lan-Cheng Wu |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 1998 | |
| 300 | |a XIII, 246 S. | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 174 | |
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Datensatz im Suchindex
| _version_ | 1804126820245700608 |
|---|---|
| adam_text | Contents
Preface to the English Translation xj
Preface xm
Part I. Second Order Elliptic Equations 1
Chapter 1. L2 Theory 3
1. Lax Milgram theorem 3
2. Weak solutions of elliptic equations 4
3. The Fredholm Alternative 7
4. A maximum principle for weak solutions 8
5. Regularity for weak solutions 13
Chapter 2. Schauder Theory 17
1. Holder spaces j
2. Mollifiers 20
3. C2 a estimates for solutions of potential equations 23
4. Interior Schauder estimates 27
5. Global Schauder estimates 30
6. A maximum principle for classical solutions 32
7. Solvability of the Dirichlet problem 33
Chapter 3. Lp Theory 37
1. The Marcinkiewicz interpolation theorem 37
2. A decomposition lemma 40
3. Estimates for solutions of potential equations 41
4. Interior W2 p estimates 46
5. Global W2 p estimates 47
6. Existence of W2 p solutions 49
Chapter 4. De Giorgi Nash Moser Estimates 53
1. Local properties of weak solutions 53
2. Interior Holder continuity 60
3. Global Holder continuity 63
Chapter 5. Quasilinear Equations of Divergence Form 67
1. Boundedness of weak solutions 67
vii
viii CONTENTS
2. Holder estimates for bounded weak solutions 69
3. Gradient estimates 72
4. Gradient Holder estimates 74
5. Solvability of the Dirichlet problem 76
Chapter 6. Krylov Safonov Estimates 79
1. The Alexandroff Bakelman Pucci maximum principle 79
2. Harnack inequalities and interior Holder estimates 87
3. Global Holder estimates 96
Chapter 7. Fully Nonlinear Elliptic Equations 99
1. Maximum norm and Holder estimates for solutions 100
2. Gradient estimates 104
3. Gradient Holder estimates 107
4. Solvability for quasilinear equations of nondivergence form 113
5. Solvability for fully nonlinear equations 115
6. A special class of equations 117
7. General fully nonlinear equations 122
Part II. Second Order Elliptic Systems 129
Chapter 8. L2 Theory for Linear Elliptic Systems of Divergence Form 131
1. Existence of weak solutions 131
2. Energy estimates and H2 regularity 134
Chapter 9. Schauder Theory for Linear Elliptic Systems of Divergence Form 137
1. Morrey and Campanato spaces 137
2. Schauder theory 145
Chapter 10. Lp Theory for Linear Elliptic Systems of Divergence Form 155
1. BMO spaces and the Stampacchia interpolation theorem 155
2. W theory 156
Chapter 11. Existence of Weak Solutions of Nonlinear Elliptic Systems 163
1. Introduction 163
2. The variational method 164
Chapter 12. Regularity for Weak Solutions of Nonlinear Elliptic Systems 173
1. H2 regularity 173
2. Further regularity and counterexamples 178
3. Indirect method for studying regularity 181
4. The reverse Holder inequality and Lp estimates for Du 187
5. Direct methods for studying regularity 198
6. The singular set 204
CONTENTS ix
Appendix 1. Sobolev Spaces 209
1. Weak derivatives and the Sobolev space Wk p(Q) 209
2. Real exponent Sobolev spaces Hs(Rn) 212
3. Poincare s inequality 213
Appendix 2. Sard s Theorem 215
Appendix 3. Proof of the John Nirenberg Theorem 217
Appendix 4. Proof of the Stampacchia Interpolation Theorem 219
Appendix 5. Proof of the Reverse Holder Inequality 225
Bibliographic Notes 233
Bibliography 239
Index 245
|
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| dewey-search | 515/.353 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV012202925 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:23:31Z |
| institution | BVB |
| isbn | 0821809709 |
| language | English Chinese |
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| physical | XIII, 246 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Chen, Ya-Zhe Verfasser aut Erh chieh t'o yüan hsing fang ch'eng yü t'o yüan hsing fang ch'eng tsu Second order elliptic equations and elliptic systems Ya-Zhe Chen ; Lan-Cheng Wu Providence, R.I. American Mathematical Society 1998 XIII, 246 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 174 Aus dem Chines. übers. Differential equations, Elliptic Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Ordnung 2 (DE-588)4350619-7 gnd rswk-swf Elliptisches System (DE-588)4121184-4 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Ordnung 2 (DE-588)4350619-7 s DE-604 Elliptisches System (DE-588)4121184-4 s Wu, Lan-Cheng Verfasser aut Translations of mathematical monographs 174 (DE-604)BV000002394 174 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008269201&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Ya-Zhe Wu, Lan-Cheng Second order elliptic equations and elliptic systems Translations of mathematical monographs Differential equations, Elliptic Elliptische Differentialgleichung (DE-588)4014485-9 gnd Ordnung 2 (DE-588)4350619-7 gnd Elliptisches System (DE-588)4121184-4 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4350619-7 (DE-588)4121184-4 |
| title | Second order elliptic equations and elliptic systems |
| title_alt | Erh chieh t'o yüan hsing fang ch'eng yü t'o yüan hsing fang ch'eng tsu |
| title_auth | Second order elliptic equations and elliptic systems |
| title_exact_search | Second order elliptic equations and elliptic systems |
| title_full | Second order elliptic equations and elliptic systems Ya-Zhe Chen ; Lan-Cheng Wu |
| title_fullStr | Second order elliptic equations and elliptic systems Ya-Zhe Chen ; Lan-Cheng Wu |
| title_full_unstemmed | Second order elliptic equations and elliptic systems Ya-Zhe Chen ; Lan-Cheng Wu |
| title_short | Second order elliptic equations and elliptic systems |
| title_sort | second order elliptic equations and elliptic systems |
| topic | Differential equations, Elliptic Elliptische Differentialgleichung (DE-588)4014485-9 gnd Ordnung 2 (DE-588)4350619-7 gnd Elliptisches System (DE-588)4121184-4 gnd |
| topic_facet | Differential equations, Elliptic Elliptische Differentialgleichung Ordnung 2 Elliptisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008269201&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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