Timeline for Showing $H^1(\partial\Omega) \subset H^{\frac 12}(\partial\Omega)$ is continuous?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Dec 17, 2018 at 15:35 | review | Close votes | |||
| Dec 22, 2018 at 3:05 | |||||
| Dec 17, 2018 at 15:20 | comment | added | Denis Serre | The question seems to be flawed. Nobody is interesting in an embedding $H^1\subset H^{1/2}$. People are instead interested into trace theorems stating that the restriction $u\mapsto u|_{\partial\Omega}$ extends continuously as an operator $\gamma_0:H^1(\Omega)\rightarrow H^{1/2}(\partial\Omega)$. Would you reformulate your question ? | |
| Dec 17, 2018 at 15:12 | answer | added | Piotr Hajlasz | timeline score: 2 | |
| Dec 19, 2014 at 9:01 | answer | added | Jean Van Schaftingen | timeline score: 3 | |
| Jan 23, 2014 at 14:36 | vote | accept | soup | ||
| Jan 19, 2014 at 16:44 | answer | added | Delio Mugnolo | timeline score: 3 | |
| Jan 17, 2014 at 21:16 | history | edited | soup | CC BY-SA 3.0 |
added 56 characters in body; edited tags
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| Jan 16, 2014 at 12:49 | comment | added | soup | @AthanagorWurlitzer Hmm, I think: around each point of the boundary, there is a neighbourhood $U_i$ and a Lipschitz function $f_i:U_i \to D_i \subset \mathbb{R}^n$. Then the norm of a function $u$ can be defined as the $H^1$ norm of the sum of the functions $u \circ f_i^{-1}$ (probably need a partition of unity somewhere) | |
| Jan 16, 2014 at 12:39 | comment | added | username | And what norm to you use for $H^1(\partial\Omega)$? | |
| S Jan 15, 2014 at 15:32 | history | suggested | smyrlis | CC BY-SA 3.0 |
It is important to specify from the beginning that $\Omega\subset\mathbb R^n$.
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| Jan 15, 2014 at 15:29 | review | Suggested edits | |||
| S Jan 15, 2014 at 15:32 | |||||
| Jan 15, 2014 at 15:15 | history | edited | soup | CC BY-SA 3.0 |
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| Jan 15, 2014 at 15:13 | comment | added | soup | @AthanagorWurlitzer Yes it is identity map $i:H^1(\partial\Omega) \to H^{\frac 12}(\partial\Omega)$. Note the norms are different (I added some details). | |
| Jan 15, 2014 at 15:11 | comment | added | username | Isn't the map in question simply the identity map? | |
| Jan 15, 2014 at 15:06 | history | asked | soup | CC BY-SA 3.0 |