The Monge-Ampère equation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2001
|
| Series: | Progress in nonlinear differential equations and their applications
44 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XI, 126 S. |
| ISBN: | 0817641777 3764341777 9781461266563 |
Staff View
MARC
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| 100 | 1 | |a Gutiérrez, Cristian E. |d 1950- |e Verfasser |0 (DE-588)104378408X |4 aut | |
| 245 | 1 | 0 | |a The Monge-Ampère equation |c Cristian E. Gutiérrez |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XI, 126 S. | ||
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| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 44 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Notation xi
1 Generalized Solutions to Monge Ampere Equations 1
1.1 The normal mapping 1
1.1.1 Properties of the normal mapping 2
1.2 Generalized solutions 6
1.3 Viscosity solutions 8
1.4 Maximum principles 10
1.4.1 Aleksandrov s maximum principle 11
1.4.2 Aleksandrov Bakelman Pucci s maximum principle ... 12
1.4.3 Comparison principle 16
1.5 The Dirichlet problem 17
1.6 The nonhomogeneous Dirichlet problem 19
1.7 Return to viscosity solutions 24
1.8 Ellipsoids of minimum volume 25
1.9 Notes 29
2 Uniformly Elliptic Equations in Nondivergence Form 31
2.1 Critical density estimates 31
2.2 Estimate of the distribution function of solutions 37
2.3 Harnack s inequality 40
2.4 Notes 43
3 The Cross sections of Monge Ampere 45
3.1 Introduction 45
3.2 Preliminary results 47
3.3 Properties of the sections 50
3.3.1 The Monge Ampere measures satisfying (3.1.1) 50
3.3.2 The engulfing property of the sections 55
3.3.3 The size of normalized sections 57
3.4 Notes 62
viii Contents
4 Convex Solutions of det D2u = 1 in W 63
4.1 Pogorelov s Lemma 63
4.2 Interior Holder estimates of D2u 67
4.3 C estimates of D2u 70
4.4 Notes 74
5 Regularity Theory for the Monge Ampere Equation 75
5.1 Extremal points 75
5.2 A result on extremal points of zeroes of solutions
to Monge Ampere 77
5.3 A strict convexity result 79
5.4 CUa regularity 84
5.5 Examples 92
5.6 Notes 93
6 W2iP Estimates for the Monge Ampere Equation 95
6.1 Approximation Theorem 95
6.2 Tangent paraboloids 99
6.3 Density estimates and power decay 101
6.4 Lp estimates of second derivatives 108
6.5 Proof of the Covering Theorem 6.3.3 112
6.6 Regularity of the convex envelope 119
6.7 Notes 121
Bibliography 123
Index 127
|
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| author | Gutiérrez, Cristian E. 1950- |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013864234 |
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| indexdate | 2024-07-09T18:53:23Z |
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| isbn | 0817641777 3764341777 9781461266563 |
| language | English |
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| physical | XI, 126 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Gutiérrez, Cristian E. 1950- Verfasser (DE-588)104378408X aut The Monge-Ampère equation Cristian E. Gutiérrez Boston [u.a.] Birkhäuser 2001 XI, 126 S. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 44 Hier auch später erschienene, unveränderte Nachdrucke Monge-Ampère, Équations de Monge-Ampère equations Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd rswk-swf Monge-Ampère-Differentialgleichung (DE-588)4253327-2 s DE-604 Progress in nonlinear differential equations and their applications 44 (DE-604)BV007934389 44 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009483258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gutiérrez, Cristian E. 1950- The Monge-Ampère equation Progress in nonlinear differential equations and their applications Monge-Ampère, Équations de Monge-Ampère equations Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd |
| subject_GND | (DE-588)4253327-2 |
| title | The Monge-Ampère equation |
| title_auth | The Monge-Ampère equation |
| title_exact_search | The Monge-Ampère equation |
| title_full | The Monge-Ampère equation Cristian E. Gutiérrez |
| title_fullStr | The Monge-Ampère equation Cristian E. Gutiérrez |
| title_full_unstemmed | The Monge-Ampère equation Cristian E. Gutiérrez |
| title_short | The Monge-Ampère equation |
| title_sort | the monge ampere equation |
| topic | Monge-Ampère, Équations de Monge-Ampère equations Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd |
| topic_facet | Monge-Ampère, Équations de Monge-Ampère equations Monge-Ampère-Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009483258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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