Timeline for Using the Rellich-Kondrachov theorem to prove Poincare inequality for a function vanishing at one point
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2017 at 17:16 | vote | accept | Shuhao Cao | ||
| Feb 19, 2017 at 16:31 | answer | added | Nate Eldredge | timeline score: 4 | |
| Feb 19, 2017 at 15:38 | comment | added | Shuhao Cao | @almaz Any references? Thanks. | |
| Feb 19, 2017 at 15:36 | history | edited | Shuhao Cao | CC BY-SA 3.0 |
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| Feb 19, 2017 at 15:29 | comment | added | Shuhao Cao | @NateEldredge Yes. | |
| Feb 19, 2017 at 13:52 | comment | added | anonymous | To build a bit upon what @almaz said: In one dimension, we have the embedding $W^{1,p}(\Omega) \subset C(\Omega)$. Point evaluations (i.e., integration w.r.t. a Dirac measure) are continuous functionals on $C(\Omega)$, regardless of the dimension. With the aforementioned embedding, in one dimension, they are also (well-defined) continuous functionals on $W^{1,p}(\Omega)$, so that their respective kernel is closed, and we can factor with respect to those kernels. The functional $f \mapsto \int_U f$ in well-defined and continuous on $W^{1,p}(\Omega)$ regardless of the dimension. | |
| Feb 19, 2017 at 5:54 | comment | added | Nate Eldredge | Does $|u|_{W^{1,p}}$ here denote $\left(\int |\nabla u|^p\right)^{1/p}$? | |
| Feb 19, 2017 at 5:29 | comment | added | ABMath | The proposition is true only in dimension 1. In higher dimensions, a constant function can be approximated in the Sobolev norm by continuous functions vanishing at finitely many points | |
| Feb 19, 2017 at 4:07 | history | asked | Shuhao Cao | CC BY-SA 3.0 |