Timeline for Smooth Sobolev extension from $W^{1,p}(U)$ to $W^{1,p} (\mathbb{R}^n) $
Current License: CC BY-SA 3.0
5 events
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| Aug 6, 2021 at 5:54 | comment | added | Rajesh D | I am looking for an extension over a Torus $\mathbb{T}^n$ instead of $\mathbb{R}^n$. Please see this question: mathoverflow.net/q/401090/14414 Appreciate any comments/references. | |
| Jul 28, 2018 at 8:22 | comment | added | Piero D'Ancona | I think the elementary counterexamples are all of finite perimeter | |
| Jul 27, 2018 at 20:24 | comment | added | Pedro Lauridsen Ribeiro | More generally, if a bounded set $\Omega$ is regularly open (i.e. $\Omega=\mathrm{int}(\overline{\Omega})$) and has finite perimeter (i.e. its characteristic function $1_\Omega$ is of bounded variation), does it satisfy the extension property? I've required $\Omega$ to be regularly open so that its reduced boundary $\partial^*\Omega$ satisfies $\overline{\partial^*\Omega}=\partial\Omega$ and therefore $\partial\Omega\smallsetminus\partial^*\Omega$ is as small as possible. | |
| Apr 22, 2012 at 10:17 | history | edited | Piero D'Ancona | CC BY-SA 3.0 |
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| Apr 22, 2012 at 0:09 | history | answered | Piero D'Ancona | CC BY-SA 3.0 |