Timeline for Positive part of Cauchy sequence of Sobolev functions is again Cauchy
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Jan 29, 2022 at 9:02 | comment | added | Denis Serre | If my memory is correct, Pietro's argument, which works for every Lipschitz function, is due to G. Stampacchia. | |
| Jan 28, 2022 at 22:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 30, 2021 at 21:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 2, 2021 at 20:05 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 2, 2021 at 21:01 | comment | added | Denis Serre | More generally, the following is true: if $\phi:{\mathbb R}\rightarrow{\mathbb R}$ is globally Lipschitz, then $f\mapsto\phi\circ f$ maps $W^{1,p}(B)$ into itself continuously. In particular, if $(f_k)_k$ is Cauchy, then so is $(\phi\circ f_k)_k$. | |
| Feb 2, 2021 at 20:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| S Jan 3, 2021 at 19:57 | history | suggested | markvs | CC BY-SA 4.0 |
fixed misprints
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| Jan 3, 2021 at 19:13 | comment | added | markvs | I have fixed a misprint in the title. Sobolev was as much a real person as Cauchy. | |
| Jan 3, 2021 at 19:12 | review | Suggested edits | |||
| S Jan 3, 2021 at 19:57 | |||||
| Jan 3, 2021 at 19:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 5, 2020 at 18:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 18, 2020 at 13:21 | comment | added | leo monsaingeon | And as Pietro mentioned, the proof goes by approximation (of $F=\lim F_\epsilon$) | |
| May 18, 2020 at 13:19 | comment | added | leo monsaingeon | I think Pietro meant "positive part $f^+=\max\{f,0\}$", and not "absolute value $|f|$". Anyway, this is true because the composition $F(f)$ of $1$-Lipschitz maps $F$ satisfying $F(0)=0$ and Sobolev maps $f\in W^{1,p}$ (including $p=1$) is again Sobolev, with $\|F(f)\|_{W^{1,p}}\leq \|f\|_{W^{1,p}}$ | |
| May 8, 2020 at 17:05 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 9, 2020 at 17:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 10, 2019 at 16:57 | answer | added | Bazin | timeline score: 1 | |
| Dec 4, 2019 at 8:05 | comment | added | Pietro Majer | In other words, $F_:f\mapsto |f|$ is a continuous self-map of $W^{1,p}(B)$. One way to show it is approximating with $F_\epsilon:f\mapsto |f^2+\epsilon^2|^{1/2}$ and letting $\epsilon\to0$ | |
| Dec 4, 2019 at 7:14 | history | asked | BremerH | CC BY-SA 4.0 |