The Monge-Ampère Equation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2001
|
| Schriftenreihe: | Progress in Nonlinear Differential Equations and Their Applications
44 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In recent years, the study of the Monge-Ampere equation has received considerable attention and there have been many important advances. As a consequence there is nowadays much interest in this equation and its applications. This volume tries to reflect these advances in an essentially self-contained systematic exposition of the theory of weak: solutions, including recent regularity results by L. A. Caffarelli. The theory has a geometric flavor and uses some techniques from harmonic analysis such us covering lemmas and set decompositions. An overview of the contents of the book is as follows. We shall be concerned with the Monge-Ampere equation, which for a smooth function u, is given by (0.0.1) There is a notion of generalized or weak solution to (0.0.1): for u convex in a domain n, one can define a measure Mu in n such that if u is smooth, then Mu 2 has density det D u. Therefore u is a generalized solution of (0.0.1) if M u = f |
| Beschreibung: | 1 Online-Ressource (XI, 132 p) |
| ISBN: | 9781461201953 9781461266563 |
| DOI: | 10.1007/978-1-4612-0195-3 |
Internformat
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| 490 | 1 | |a Progress in Nonlinear Differential Equations and Their Applications |v 44 | |
| 500 | |a In recent years, the study of the Monge-Ampere equation has received considerable attention and there have been many important advances. As a consequence there is nowadays much interest in this equation and its applications. This volume tries to reflect these advances in an essentially self-contained systematic exposition of the theory of weak: solutions, including recent regularity results by L. A. Caffarelli. The theory has a geometric flavor and uses some techniques from harmonic analysis such us covering lemmas and set decompositions. An overview of the contents of the book is as follows. We shall be concerned with the Monge-Ampere equation, which for a smooth function u, is given by (0.0.1) There is a notion of generalized or weak solution to (0.0.1): for u convex in a domain n, one can define a measure Mu in n such that if u is smooth, then Mu 2 has density det D u. Therefore u is a generalized solution of (0.0.1) if M u = f | ||
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Datensatz im Suchindex
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| author | Gutiérrez, Cristian E. 1950- |
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| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0195-3 |
| format | Electronic eBook |
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| id | DE-604.BV042419476 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781461201953 9781461266563 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854893 |
| oclc_num | 869873249 |
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| physical | 1 Online-Ressource (XI, 132 p) |
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| 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 by Cristian E. Gutiérrez Boston, MA Birkhäuser Boston 2001 1 Online-Ressource (XI, 132 p) txt rdacontent c rdamedia cr rdacarrier Progress in Nonlinear Differential Equations and Their Applications 44 In recent years, the study of the Monge-Ampere equation has received considerable attention and there have been many important advances. As a consequence there is nowadays much interest in this equation and its applications. This volume tries to reflect these advances in an essentially self-contained systematic exposition of the theory of weak: solutions, including recent regularity results by L. A. Caffarelli. The theory has a geometric flavor and uses some techniques from harmonic analysis such us covering lemmas and set decompositions. An overview of the contents of the book is as follows. We shall be concerned with the Monge-Ampere equation, which for a smooth function u, is given by (0.0.1) There is a notion of generalized or weak solution to (0.0.1): for u convex in a domain n, one can define a measure Mu in n such that if u is smooth, then Mu 2 has density det D u. Therefore u is a generalized solution of (0.0.1) if M u = f Mathematics Differential equations, partial Global differential geometry Partial Differential Equations Applications of Mathematics Differential Geometry Mathematik Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd rswk-swf Monge-Ampère-Differentialgleichung (DE-588)4253327-2 s 1\p DE-604 Progress in Nonlinear Differential Equations and Their Applications 44 (DE-604)BV036582883 44 https://doi.org/10.1007/978-1-4612-0195-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gutiérrez, Cristian E. 1950- The Monge-Ampère Equation Progress in Nonlinear Differential Equations and Their Applications Mathematics Differential equations, partial Global differential geometry Partial Differential Equations Applications of Mathematics Differential Geometry Mathematik 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 by Cristian E. Gutiérrez |
| title_fullStr | The Monge-Ampère Equation by Cristian E. Gutiérrez |
| title_full_unstemmed | The Monge-Ampère Equation by Cristian E. Gutiérrez |
| title_short | The Monge-Ampère Equation |
| title_sort | the monge ampere equation |
| topic | Mathematics Differential equations, partial Global differential geometry Partial Differential Equations Applications of Mathematics Differential Geometry Mathematik Monge-Ampère-Differentialgleichung (DE-588)4253327-2 gnd |
| topic_facet | Mathematics Differential equations, partial Global differential geometry Partial Differential Equations Applications of Mathematics Differential Geometry Mathematik Monge-Ampère-Differentialgleichung |
| url | https://doi.org/10.1007/978-1-4612-0195-3 |
| volume_link | (DE-604)BV036582883 |
| work_keys_str_mv | AT gutierrezcristiane themongeampereequation |