Timeline for Double calculus of variations [closed]
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 21, 2017 at 14:41 | comment | added | gappy3000 | Thanks. Very helpful. The only book I had is Ewing's Calculus of Variations. | |
| Mar 21, 2017 at 14:39 | vote | accept | gappy3000 | ||
| Mar 21, 2017 at 12:34 | history | closed |
Michael Renardy Jan-Christoph Schlage-Puchta Sebastian Goette Ben McKay José Figueroa-O'Farrill |
Not suitable for this site | |
| Mar 21, 2017 at 3:01 | answer | added | Rodrigo de Azevedo | timeline score: 1 | |
| Mar 20, 2017 at 23:17 | comment | added | Igor Khavkine | If you have never studied calculus of variations with multiple independent variables, it's hard to say where to start. You can find quite a thorough treatment in Giaquinta & Hildebrandt's Calculus of Variations (vol. I)[dx.doi.org/10.1007/978-3-662-03278-7] and (vol. II)[dx.doi.org/10.1007/978-3-662-06201-2]. However, depending on your background, this may or may not be easy reading. | |
| Mar 20, 2017 at 21:50 | comment | added | gappy3000 | I think you replace integration by part with divergence when you deal with problems in many variables. In this case the problem is in a single variable, $x$. | |
| Mar 20, 2017 at 19:37 | comment | added | Paul Siegel | Necessary and sufficient conditions are not easy in either case, but the same procedure which produces necessary conditions (the Euler equations) in the one variable case also works in the two variable case - you just have to replace the integration by parts step with the divergence theorem. There are similar sufficient conditions involving the Legendre test etc. but they are generally a bit more complicated because boundary value problems are hard. | |
| Mar 20, 2017 at 18:24 | review | Close votes | |||
| Mar 21, 2017 at 7:22 | |||||
| Mar 20, 2017 at 18:06 | comment | added | Michael Renardy | There is an enormous literature on calculus of variations for multiple integrals. Even some of the Hilbert problems came from this field! | |
| Mar 20, 2017 at 18:01 | history | edited | gappy3000 | CC BY-SA 3.0 |
generalized problem and made it clearer
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| Mar 20, 2017 at 17:41 | history | asked | gappy3000 | CC BY-SA 3.0 |