Timeline for Reference request: theory for local minimizers in the calculus of variations
Current License: CC BY-SA 4.0
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| Feb 23, 2023 at 10:56 | comment | added | mlk | To add to this, a similar definition is quite common in the theory of minimal surfaces, which often deals with non-compact surfaces (e.g. Simon's cone). Also the name "local minimizer" is normally used to talk about functions $f$ that minimize the full integral in some neighborhood of $f$ in $X$. | |
| Feb 22, 2023 at 23:51 | comment | added | user378654 | To get useful answers to this you would need to be more specific. Regularity in this context is not particularly interesting, the theory is the same as in the compact case. The main difficulty is existence vs. nonexistence and behavior of minimizing sequences. A reasonable starting point might be the series of papers by P.L. Lions, "The concentration-compactness principle in the calculus of variations," which has many examples. | |
| Feb 22, 2023 at 22:22 | review | Close votes | |||
| Mar 21, 2023 at 3:04 | |||||
| S Feb 22, 2023 at 21:13 | review | First questions | |||
| Feb 22, 2023 at 22:24 | |||||
| S Feb 22, 2023 at 21:13 | history | asked | Franlezana | CC BY-SA 4.0 |