Timeline for On a Poincaré inequality with weight
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2023 at 13:04 | history | became hot network question | |||
| Sep 19, 2023 at 10:44 | comment | added | Eric Arnéo Vespira Kengne | Also, perhaps the reference sciencedirect.com/science/article/pii/S0019357720300318 and reference therein could help you on some relationship between weight. I didn't truly go through. | |
| Sep 19, 2023 at 10:41 | answer | added | Michele Caselli | timeline score: 5 | |
| Sep 19, 2023 at 10:26 | comment | added | Eric Arnéo Vespira Kengne | As $\Omega$ is convex and bounded and as we are in flat space, a good deal of the problem is about the regularity (in fact, the geometric structure) of its boundary, I think. Also, I think that $p$ can't be arbitrary, as I'm seeing the weight $\omega$ as a family of riemannian metrics on the boundary. A consequence of this later view entails the study of the weight at some "characteristic" inner point of $\Omega$. This make the link with capacity theory, and then, with quasiconformal geometry, and then... | |
| Sep 19, 2023 at 9:59 | comment | added | Romain Gicquaud | @AndréSchlichting: No, there is no weight in the definition of $L^q$. I want to compare $f$ with its average value (w.r.t. $\omega$) in the standard $L^q$-norm. | |
| Sep 19, 2023 at 9:50 | comment | added | André Schlichting | Is the weight only entering the average $f_\omega$ or does it also enter the norm $L^q(\Omega)$? Typically weighted Poincaré inequalities are stated in $L^q(\omega)$. | |
| Sep 19, 2023 at 9:12 | comment | added | Romain Gicquaud | @GiorgioMetafune: Thank you very much for pointing these oversights! I corrected my question accordingly. | |
| Sep 19, 2023 at 9:11 | history | edited | Romain Gicquaud | CC BY-SA 4.0 |
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| Sep 19, 2023 at 8:42 | comment | added | Giorgio Metafune | Are $p,q$ conjugate? Do you want $C$ to be independent of the weight? | |
| Sep 19, 2023 at 0:08 | history | asked | Romain Gicquaud | CC BY-SA 4.0 |