Timeline for Is this property preserved under weak$^*$ convergence?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 14 at 6:41 | comment | added | Giorgio Metafune | You may apply Fatou lemma to the sequence $|u_m-\bar u_m|^{p^*} \chi_{B_m}$ or fix a compact $K$ and apply Fatou to $|u_m-\bar u_m|^{p^*}$ in $K$ and then take the supremum on all $K$. | |
| Sep 13 at 22:16 | comment | added | Cauchy's Sequence | Can you explain how you deduce that $u$ is in $L^{p^*}$? I don't think one can simply take the limit in the Poincaré inequality but perhaps I am missing something. | |
| Aug 31 at 15:14 | history | edited | Giorgio Metafune | CC BY-SA 4.0 |
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| Aug 31 at 12:56 | comment | added | Cauchy's Sequence | Oh sorry, I didn't notice the $p^*$. So you actually prove that the limit is in $L^{p^*}$. That's interesting. Thanks! Do you expect the statement to hold more generally? | |
| Aug 31 at 12:04 | comment | added | Giorgio Metafune | This is not Poincarè $p \to p$ but $p \to p^*$. | |
| Aug 31 at 11:53 | comment | added | Cauchy's Sequence | The Poincaré constant isn't scale invariant. It scales like $r$, with $r$ being the radius. | |
| Aug 31 at 10:37 | history | answered | Giorgio Metafune | CC BY-SA 4.0 |