Timeline for Perimeter continuity of $BV$ sets on any sequence from $W^{1,1}$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 23, 2021 at 21:29 | comment | added | Bogdan | Now I see. Thanks a lot for your answer! | |
| Jul 23, 2021 at 21:28 | vote | accept | Bogdan | ||
| Jul 23, 2021 at 20:33 | comment | added | Leo Moos | I adapted the argument according to your comments - it suggests that the counterexample I gave earlier would work for any $\omega \subset \Omega$ with bounded perimeter. | |
| Jul 23, 2021 at 20:30 | history | edited | Leo Moos | CC BY-SA 4.0 |
adapted answer according to comments.
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| Jul 23, 2021 at 16:11 | comment | added | Bogdan | Yes, with non-empty $\omega$. I try to find an example with $\omega$ being an interval (in the 1 dimensional case -which can be viewed as a two dimensional case if $y$ is not involved) by considering as you said a molliefied version of the characteristic function + something like your $f_n$. But the variantion goes to 2 also. I do not see why adding $f_n$ to a mollified characteristic function will increase the perimeter... | |
| Jul 23, 2021 at 15:43 | comment | added | Leo Moos | When you say other examples, do you mean non-empty sets $\omega$? That you can certainly get, for example by taking the sum of a mollified indicator $\mathbf{1}_\omega$ with the $f_n$ above. Could you explain what you mean when you say that you 'tried with intervals'? | |
| S Jul 23, 2021 at 15:41 | history | suggested | Bogdan | CC BY-SA 4.0 |
I modify $+\infty$ to $0$.
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| Jul 23, 2021 at 15:40 | review | Suggested edits | |||
| S Jul 23, 2021 at 15:41 | |||||
| Jul 23, 2021 at 15:38 | comment | added | Bogdan | I wonder if there are other examples. I tried with intervals but seems ok. Thanks for your example! | |
| Jul 23, 2021 at 15:25 | history | answered | Leo Moos | CC BY-SA 4.0 |