Timeline for Jet bundles and partial differential operators
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Sep 29, 2011 at 13:23 | vote | accept | Willie Wong | ||
| Sep 29, 2011 at 13:16 | history | edited | Willie Wong | CC BY-SA 3.0 |
Minor technical correction to factor in Dmitri's comment.
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| Sep 28, 2011 at 15:47 | comment | added | Willie Wong | @Deane: ah, chapter IX of the book you referred is very helpful. Thanks. | |
| Sep 28, 2011 at 15:24 | comment | added | Willie Wong | For first and second order systems one can do what I want without referring to all this abstract nonsense. But as far as I can work out this point of view is necessary if I want to deal with higher order systems of equations. | |
| Sep 28, 2011 at 15:23 | comment | added | Willie Wong |
@Deane: well, it is a bit embarrassing. In what I am working on at the moment this will be formal set-up that will end up being ¨tossed away¨; so at the moment I am just trying to cover my behind by making sure I am not saying anything irresponsible. :-) (Though this may become genuinely the focus later.) As to why I need this formal set-up: I want to get a good notion of a ¨quasilinear¨ partial differential equation independent of the choice of connection, and to define its linearisation and its linearised principal symbol.
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| Sep 28, 2011 at 14:25 | comment | added | Deane Yang | Assuming he has time, Robert Bryant is the best person to answer your question. You might want to look at the book of Bryant, Chern, Gardner, Goldschmidt, and Griffiths. Although the focus on the book is using exterior differential systems (which are equivalent to systems of PDE's as you define above), Goldschmidt approaches the subject from the jet bundle point of view. | |
| Sep 28, 2011 at 14:18 | comment | added | Deane Yang | Could you say why you're interested in such a formal setup for PDE's? | |
| Sep 28, 2011 at 12:51 | comment | added | Dmitri Pavlov | Peetre's theorem can only be stated this way for compact manifolds. For non-compact manifolds you have to allow differential operators of (globally) infinite order (locally they still have finite order). For example, you can glue a sequence of differential operators with increasing orders into one differential operator using a partition of unity. | |
| Sep 28, 2011 at 10:31 | answer | added | Michael Bächtold | timeline score: 12 | |
| Sep 28, 2011 at 9:07 | history | asked | Willie Wong | CC BY-SA 3.0 |