Timeline for Reference or proof of a lemma in PDE
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14, 2022 at 14:03 | vote | accept | Partha | ||
| Sep 11, 2022 at 13:07 | answer | added | Scott Armstrong | timeline score: 5 | |
| Sep 3, 2022 at 12:24 | answer | added | username | timeline score: 3 | |
| Sep 3, 2022 at 9:30 | comment | added | username | @GiorgioMetafune : Oops you are right it shows $L^p$ not $W^{1,p}$ my mistake (I deleted it). Yes, you need something more, and for $p>1$ the fact that $\Delta : W^{1,,p}_0(B_2) -> W^{-1,p}(B_2)$ is invertible with continuous inverse is enough, but that isn't variational. I don't think it is true for $p=1$ in every dimension (2 could be special). | |
| Sep 2, 2022 at 18:54 | comment | added | Giorgio Metafune | He means the norm in the Sobolev space $W^{1,p}$; $C$ is independent of $f$. | |
| Sep 2, 2022 at 18:49 | comment | added | username | what is $\| \cdot \|_{L^p_1(B_1)}$ ? If it is just $\| \cdot \|_{L^p(B_1)}$, it is trivial, since $\| f \|_{L^p(B_1)} \leq \| f \|_{L^p(B_2)} $. You must mean something else. | |
| Sep 2, 2022 at 18:41 | comment | added | YCor | I'm confused: aren't you rather asking whether there exists $C>0$ such that for all $f,F$ the inequality holds? otherwise just take to be $1$ if $f=0$ a.e. and $C=(\|F\|_{\dots}+\|f\|_{\dots})/\|f\|_{\dots}$ otherwise... | |
| Sep 2, 2022 at 18:39 | history | edited | YCor | CC BY-SA 4.0 |
added tag
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| Sep 2, 2022 at 17:51 | history | edited | Nawaf Bou-Rabee | CC BY-SA 4.0 |
deleted 2 characters in body
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| Sep 2, 2022 at 15:01 | answer | added | Giorgio Metafune | timeline score: 3 | |
| Sep 2, 2022 at 10:50 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing and formatting
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| Sep 2, 2022 at 8:56 | history | asked | Partha | CC BY-SA 4.0 |