Timeline for Lavrentiev phenomenon between $C^1$ + Lipschitz derivative and $C^2$
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 24, 2021 at 16:38 | vote | accept | Nate River | ||
| Jul 24, 2021 at 13:20 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jul 24, 2021 at 13:14 | history | undeleted | Alexandre Eremenko | ||
| Jul 24, 2021 at 0:57 | history | deleted | Alexandre Eremenko | via Vote | |
| Jul 24, 2021 at 0:56 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jul 23, 2021 at 23:34 | comment | added | Nate River | Oh what I meant was that if $g’$ was allowed here, we could emulate that construction with $g$ replaced by $g’$ and the proof would hold verbatim. But because we have only $g$ here, and the “regularity gap” is between $C^1$ + Lipschitz and $C^2$, the same proof won’t work. | |
| Jul 23, 2021 at 23:31 | comment | added | Leo Moos | @NateRiver I'm not sure I follow - the functional in the linked answer doesn't seem to depend on the derivative. | |
| Jul 23, 2021 at 23:14 | comment | added | Nate River | @Leo Moos - this would apply if there was a $g’$ in the argument for f, but the case where it depends only on $t, g$ is much more subtle. | |
| Jul 23, 2021 at 20:42 | comment | added | Leo Moos | Could you clarify what you intend for $f$ - there seems to be a typo? Also, the last claim seems very strong, could you provide some details? It seems a bit counterintuitive given that a $C^1$ can be approximated by $C^2$ functions. (Personally I thought that the answer given to a related question ought to apply here too.) | |
| Jul 23, 2021 at 13:26 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Jul 23, 2021 at 13:18 | history | answered | Alexandre Eremenko | CC BY-SA 4.0 |