Timeline for Sobolev interpolation inequality for relatively compact subdomains
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jan 25, 2022 at 3:01 | history | bounty ended | CommunityBot | ||
| S Jan 25, 2022 at 3:01 | history | notice removed | CommunityBot | ||
| Jan 19, 2022 at 20:53 | comment | added | Carlos Esparza | @GiorgioMetafune It seems like you're right. I feel quite stupid now for noticing that earlier. | |
| Jan 17, 2022 at 12:49 | comment | added | Giorgio Metafune | But this cannot be true as stated. Take a smooth function supported in $B_R \setminus B_r$ so that $\|u\|_{0,p, B_r}=0$ and let $\epsilon \to 0$; then you get that $u=0$. | |
| S Jan 17, 2022 at 1:34 | history | bounty started | Carlos Esparza | ||
| S Jan 17, 2022 at 1:34 | history | notice added | Carlos Esparza | Draw attention | |
| Jan 13, 2022 at 8:36 | comment | added | Hannes | Ah, that makes it more complicated :-) Sorry for not reading carefully enough. | |
| Jan 13, 2022 at 8:19 | history | edited | Carlos Esparza | CC BY-SA 4.0 |
added 57 characters in body
|
| Jan 13, 2022 at 8:18 | comment | added | Carlos Esparza | The first inequality has a $r$, not $R$ in the last term. Nicolaescu is basically claiming that the $(j, p)$-norm is controlled by $\epsilon$ times the $(m, p)$ norm plus $\epsilon^{...}$ times the norm on any compact subdomain. The result from Adams-Fournier only says some compact subdomain which might even depend on $\epsilon$. | |
| Jan 13, 2022 at 7:42 | comment | added | Hannes | Maybe I am missing something, but since $u$ is assumed to be supported in $B_R$, the $\mathbb{R}^n$ norms are the same as $B_R$ norms, and in the quoted theorem, the $\Omega_\varepsilon$ norm is surely bounded by the $\Omega$ norm, so with $\Omega = B_R$ this is it? | |
| Jan 12, 2022 at 21:50 | comment | added | Carlos Esparza | @Hannes Oh that's a mistake, thanks for pointing it out. I fixed it. | |
| Jan 12, 2022 at 21:48 | history | edited | Carlos Esparza | CC BY-SA 4.0 |
edited body
|
| Jan 12, 2022 at 15:42 | comment | added | Hannes | I am slightly confused, the proof of the first inequality (Nicolaescu version) points to the second inequality (Adams/Fournier book), yet you ask how to to get the second inequality from the first. Is that a mix up or actually the correct question? | |
| Jan 12, 2022 at 0:07 | comment | added | Carlos Esparza | I've moved this question from math.stackexchange (and deleted the question there). | |
| Jan 12, 2022 at 0:06 | history | asked | Carlos Esparza | CC BY-SA 4.0 |