The Monge-Ampère Equation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser Boston
2001
|
| Series: | Progress in Nonlinear Differential Equations and Their Applications
44 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 |
| Physical Description: | 1 Online-Ressource (XI, 132 p) |
| ISBN: | 9781461201953 9781461266563 |
| DOI: | 10.1007/978-1-4612-0195-3 |
Staff View
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042419476 | ||
| 003 | DE-604 | ||
| 005 | 20210526 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2001 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461201953 |c Online |9 978-1-4612-0195-3 | ||
| 020 | |a 9781461266563 |c Print |9 978-1-4612-6656-3 | ||
| 024 | 7 | |a 10.1007/978-1-4612-0195-3 |2 doi | |
| 035 | |a (OCoLC)869873249 | ||
| 035 | |a (DE-599)BVBBV042419476 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.353 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 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 by Cristian E. Gutiérrez |
| 264 | 1 | |a Boston, MA |b Birkhäuser Boston |c 2001 | |
| 300 | |a 1 Online-Ressource (XI, 132 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Global differential geometry | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Applications of Mathematics | |
| 650 | 4 | |a Differential Geometry | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Monge-Ampère-Differentialgleichung |0 (DE-588)4253327-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Monge-Ampère-Differentialgleichung |0 (DE-588)4253327-2 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 830 | 0 | |a Progress in Nonlinear Differential Equations and Their Applications |v 44 |w (DE-604)BV036582883 |9 44 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-0195-3 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027854893 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153090148925440 |
|---|---|
| any_adam_object | |
| author | Gutiérrez, Cristian E. 1950- |
| author_GND | (DE-588)104378408X |
| author_facet | Gutiérrez, Cristian E. 1950- |
| author_role | aut |
| author_sort | Gutiérrez, Cristian E. 1950- |
| author_variant | c e g ce ceg |
| building | Verbundindex |
| bvnumber | BV042419476 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)869873249 (DE-599)BVBBV042419476 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0195-3 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02829nmm a2200505zcb4500</leader><controlfield tag="001">BV042419476</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210526 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2001 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461201953</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-0195-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461266563</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4612-6656-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-0195-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)869873249</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042419476</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.353</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gutiérrez, Cristian E.</subfield><subfield code="d">1950-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)104378408X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Monge-Ampère Equation</subfield><subfield code="c">by Cristian E. Gutiérrez</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, MA</subfield><subfield code="b">Birkhäuser Boston</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 132 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Progress in Nonlinear Differential Equations and Their Applications</subfield><subfield code="v">44</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, partial</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Global differential geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Partial Differential Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Applications of Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Monge-Ampère-Differentialgleichung</subfield><subfield code="0">(DE-588)4253327-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Monge-Ampère-Differentialgleichung</subfield><subfield code="0">(DE-588)4253327-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Progress in Nonlinear Differential Equations and Their Applications</subfield><subfield code="v">44</subfield><subfield code="w">(DE-604)BV036582883</subfield><subfield code="9">44</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-0195-3</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027854893</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| 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 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XI, 132 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser Boston |
| 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 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 |