Timeline for Compact embedding between parabolic Hölder spaces
Current License: CC BY-SA 4.0
27 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 17, 2023 at 5:06 | 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. | |
| Jan 17, 2023 at 5:05 | 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. | |
| Sep 19, 2022 at 4:06 | 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. | |
| May 22, 2022 at 3:05 | 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 22, 2022 at 3:02 | 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 24, 2021 at 2:06 | comment | added | sharpend | This is why it would be great if somebody wrote an up-to-date and friendly version of Ladyzhenskaya-Solonnikov-Uraltseva... | |
| Sep 24, 2021 at 2:04 | 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 27, 2021 at 1:06 | 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. | |
| Jan 27, 2021 at 0:07 | 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 28, 2020 at 23:04 | 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 31, 2020 at 23:03 | 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 1, 2020 at 23:01 | 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. | |
| Oct 4, 2019 at 23:01 | 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 4, 2019 at 22:13 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title (the question was bumped anyway)
|
| Sep 4, 2019 at 22:03 | 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 7, 2019 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. | |
| Jan 7, 2019 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. | |
| Dec 8, 2018 at 20:02 | 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. | |
| Nov 8, 2018 at 19:53 | answer | added | DCM | timeline score: 1 | |
| Nov 8, 2018 at 0:31 | comment | added | DCM | The $C^{2+\alpha,\beta}(Q_T)$ in my last comment should have been a $C^{2+\alpha,1+\beta}(Q_T)$, and what I'm really interested in is whether you agree that, for $u$ in this space, $u$ and its first order $x$ and $t$ derivatives are Lipschitz continuous with respect to the metric given by $d((x,t),(x',t')) = |x-x'|^\alpha + |t-t'|^\beta$. I suspect that'll suffice, but will check and post an answer once I'm clearer on your definitions. | |
| Nov 8, 2018 at 0:01 | comment | added | DCM | Hi again. I'm not sure I'm quite clear on the definitions of your spaces. Could you perhaps confirm (or give an indication to the contrary) that all the functions in your first space $C^{2+\alpha,\beta}(Q_T)$ have $u, \dfrac{\partial u}{\partial x}, \dfrac{\partial u}{\partial t}\in C^{\alpha,\beta}(\bar Q_T)$? I think this is likely to be all you need (provided $\Omega$ is an interval or similar) to get a compact embedding here, but I'm reluctant to work on an interpolation inequality until I'm clear on what spaces you're considering. Feel free to refer me to a reference if you like :) | |
| Nov 6, 2018 at 22:23 | history | edited | YCor |
edited tags
|
|
| Nov 6, 2018 at 21:14 | comment | added | DCM | I think you should be ok if $\Omega \subset \mathbb{R}$ is a finite union of bounded open intervals (I think you may want some sort of boundary smoothness for compactness of this sort of embedding in general). I'm not sure you'll find the statement you want explicitly, but you might be able to derive it from suitable interpolation estimates. Might be worth looking what google turns up on interpolation inequalities in parabolic Holder spaces. | |
| Nov 6, 2018 at 19:59 | comment | added | VirgoMath | @DCM Yes, $\Omega$ is an open bounded interval. Do you mean that if $Q_T$ be a bounded domain, then the above embedding is compact? | |
| Nov 6, 2018 at 19:47 | comment | added | DCM | Do you mean to say that $\Omega$ is a bounded interval here? If so, isn't it the case that all the domains you're considering here are bounded rectangles (where you'll almost certainly have a compact embedding)? Unless I'm missing something, I think you should be able to get what in that setting using something like the interpolation inequality trick described here: books.google.co.uk/… | |
| Nov 6, 2018 at 14:45 | review | First posts | |||
| Nov 6, 2018 at 14:53 | |||||
| Nov 6, 2018 at 14:41 | history | asked | VirgoMath | CC BY-SA 4.0 |