Timeline for On a Poincaré inequality with weight
Current License: CC BY-SA 4.0
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| Sep 19, 2023 at 12:23 | history | edited | Michele Caselli | CC BY-SA 4.0 |
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| Sep 19, 2023 at 11:31 | comment | added | Romain Gicquaud | You can make your argument easier by using Minkowski's inequality to conclude that there exists a constant $C > 0$ such that $|f(0)| \leq \|f\|_{W^{1, q}}$. As the point $0$ has nothing special, you get that $W^{1, q}$ embeds into $L^\infty$. This rules out the possibility of choosing $q < n$. For $q > n$, the proof is fairly easy I guess using the embedding into $C^\gamma$. | |
| Sep 19, 2023 at 10:41 | history | answered | Michele Caselli | CC BY-SA 4.0 |