Timeline for Parabolic Regularity with Neumann B.C
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Feb 27, 2018 at 5:18 | history | bounty ended | username | ||
| S Feb 27, 2018 at 5:18 | history | notice removed | username | ||
| Feb 27, 2018 at 5:17 | vote | accept | username | ||
| Feb 23, 2018 at 16:34 | answer | added | Hannes | timeline score: 2 | |
| S Feb 22, 2018 at 18:35 | history | bounty started | username | ||
| S Feb 22, 2018 at 18:35 | history | notice added | username | Draw attention | |
| Feb 22, 2018 at 11:05 | comment | added | username | I would be happy to accept an answer if you write what you are thinking about in an answer form.. | |
| Feb 22, 2018 at 9:26 | comment | added | Hannes | Whoops, I think I thought in elliptic terms there, you're right of course. One should be able to get the estimate and uniformity with respect to $T$ from maximal regularity techniques in negative Sobolev spaces, the uniformity however hinges upon 0 being a spectral value of the differential operator, about which I am honestly a bit confused at the moment, but I will think about it some more.. | |
| Feb 22, 2018 at 7:50 | comment | added | username | @Hannes. There is an initial condition in time.. and the $L^1$ norm is time independent (integrate against 1), so the $+c$ cannot sneak in. | |
| S Feb 21, 2018 at 10:32 | history | suggested | Hannes | CC BY-SA 3.0 |
Fixed domain names
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| Feb 21, 2018 at 10:07 | review | Suggested edits | |||
| S Feb 21, 2018 at 10:32 | |||||
| Feb 21, 2018 at 10:05 | comment | added | Hannes | The size of the exponents I mentioned can be found e.g. in the parabolic book of Ladyzhenskaya et al, I think §3.7, but I'm not sure as to how everything there works for Neumann BC (can't check right now). Anyway, your estimate will only work if you restrict yourself to functions $u$ satisfying e.g. $\int_B u = 0$ or add "$+u$" in the equation, since otherwise for every solution $u$ to the PDE, $u + c$ for any constant (function) $c$ will also be a solution and your estimate cannot hold. I could give you a quick proof for your claim then. | |
| Feb 20, 2018 at 17:29 | comment | added | username | @Hannes. Thank you, I corrected the definition. Where can I read the proof of the statement you made (I want to check the dependence on T). | |
| Feb 20, 2018 at 17:26 | history | edited | username | CC BY-SA 3.0 |
added 120 characters in body
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| Feb 20, 2018 at 17:14 | comment | added | Hannes | I would expect $q>n$ (space dimension) and $p > 2(1-n/q)^{-1}$ as usual, the classical requirements to obtain continuous solutions. I am however a bit sceptical about the lack of boundary data for $F$ in your desired estimate, but maybe I am missing something. | |
| Feb 20, 2018 at 16:55 | history | asked | username | CC BY-SA 3.0 |