Partial Differential Relations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, A Series of Modern Surveys in Mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. Law abiding functions, which satisfy such an equation, are very rare in the space of all admissible functions (regardless of a particular topology in a function space). Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics. Our equations are, for the most part, undetermined (or, at least, behave like those) and their solutions are rather dense in spaces of functions. We solve and classify solutions of these equations by means of direct (and not so direct) geometric constructions. Our exposition is elementary and the proofs of the basic results are selfcontained. However, there is a number of examples and exercises (of variable difficulty), where the treatment of a particular equation requires a certain knowledge of pertinent facts in the surrounding field. The techniques we employ, though quite general, do not cover all geometrically interesting equations. The border of the unexplored territory is marked by a number of open questions throughout the book |
| Beschreibung: | 1 Online-Ressource (IX, 363 p) |
| ISBN: | 9783662022672 9783642057205 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-662-02267-2 |
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Datensatz im Suchindex
| _version_ | 1804153098620370944 |
|---|---|
| any_adam_object | |
| author | Gromov, Mikhael |
| author_facet | Gromov, Mikhael |
| author_role | aut |
| author_sort | Gromov, Mikhael |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | BV042423191 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863887018 (DE-599)BVBBV042423191 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-02267-2 |
| format | Electronic eBook |
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| id | DE-604.BV042423191 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783662022672 9783642057205 |
| issn | 0071-1136 |
| language | English |
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| oclc_num | 863887018 |
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| physical | 1 Online-Ressource (IX, 363 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, A Series of Modern Surveys in Mathematics |
| spelling | Gromov, Mikhael Verfasser aut Partial Differential Relations by Mikhael Gromov Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (IX, 363 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, A Series of Modern Surveys in Mathematics 9 0071-1136 The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. Law abiding functions, which satisfy such an equation, are very rare in the space of all admissible functions (regardless of a particular topology in a function space). Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics. Our equations are, for the most part, undetermined (or, at least, behave like those) and their solutions are rather dense in spaces of functions. We solve and classify solutions of these equations by means of direct (and not so direct) geometric constructions. Our exposition is elementary and the proofs of the basic results are selfcontained. However, there is a number of examples and exercises (of variable difficulty), where the treatment of a particular equation requires a certain knowledge of pertinent facts in the surrounding field. The techniques we employ, though quite general, do not cover all geometrically interesting equations. The border of the unexplored territory is marked by a number of open questions throughout the book Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Immersion Differentialgeometrie (DE-588)4191446-6 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Einbettung Mathematik (DE-588)4151233-9 gnd rswk-swf Immersion Topologie (DE-588)4161350-8 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Partielle Differentialgleichung (DE-588)4044779-0 s Immersion Topologie (DE-588)4161350-8 s 1\p DE-604 Einbettung Mathematik (DE-588)4151233-9 s 2\p DE-604 Immersion Differentialgeometrie (DE-588)4191446-6 s 3\p DE-604 https://doi.org/10.1007/978-3-662-02267-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gromov, Mikhael Partial Differential Relations Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Immersion Differentialgeometrie (DE-588)4191446-6 gnd Differentialgeometrie (DE-588)4012248-7 gnd Einbettung Mathematik (DE-588)4151233-9 gnd Immersion Topologie (DE-588)4161350-8 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4191446-6 (DE-588)4012248-7 (DE-588)4151233-9 (DE-588)4161350-8 |
| title | Partial Differential Relations |
| title_auth | Partial Differential Relations |
| title_exact_search | Partial Differential Relations |
| title_full | Partial Differential Relations by Mikhael Gromov |
| title_fullStr | Partial Differential Relations by Mikhael Gromov |
| title_full_unstemmed | Partial Differential Relations by Mikhael Gromov |
| title_short | Partial Differential Relations |
| title_sort | partial differential relations |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Immersion Differentialgeometrie (DE-588)4191446-6 gnd Differentialgeometrie (DE-588)4012248-7 gnd Einbettung Mathematik (DE-588)4151233-9 gnd Immersion Topologie (DE-588)4161350-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Partielle Differentialgleichung Immersion Differentialgeometrie Differentialgeometrie Einbettung Mathematik Immersion Topologie |
| url | https://doi.org/10.1007/978-3-662-02267-2 |
| work_keys_str_mv | AT gromovmikhael partialdifferentialrelations |