Timeline for Possible way to define $H_0^1(\Omega)$ Sobolev spaces
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 8, 2022 at 15:57 | comment | added | Willie Wong | @GuyFsone: by Morrey's inequality every element in $H^1_0(\Omega)$ is almost everywhere equal to a continuous function that vanishes at $0$. So a smooth bump function that does not vanish at $0$ is an element of $H^1(\mathbb{R})$ but not in $H^1_0(\Omega)$. | |
| Nov 8, 2022 at 12:06 | comment | added | Guy Fsone | please how do you show that the inclusion is strict? | |
| S Nov 7, 2022 at 3:11 | history | suggested | Guy Fsone | CC BY-SA 4.0 |
the inclusion was wrongly placed
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| Nov 6, 2022 at 20:03 | review | Suggested edits | |||
| S Nov 7, 2022 at 3:11 | |||||
| Nov 6, 2022 at 19:50 | vote | accept | Guy Fsone | ||
| Apr 8, 2022 at 17:44 | comment | added | Willie Wong | Your next question would be: when is $\Omega$ a Sobolev extension domain? It is sufficient that $\Omega$ has Lipschitz boundary. But I don't think there is a known (useful) characterization result. | |
| Apr 8, 2022 at 17:41 | history | answered | Willie Wong | CC BY-SA 4.0 |