Timeline for Dense set in Sobolev space ${H^1}\left( {0,1} \right)$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Sep 14, 2019 at 14:54 | comment | added | Pietro Majer | I like them all, yet I think the true proof of the plain density claim is number 2. We may also apply the lemma to $u\mapsto u'(0)$ as a discontinuous linear functional say on $H^2\cap H^1_0([0,1/10])$ with the $H^1$-norm. As a consequence, arbitrarily close to any function $v\in H^2(0,1)$ wrto the $H^1$ distance there is a function $w\in H^2(0,1)$ with arbitrary derivative at $0$ (and with $v=w$ on $[1/10,1]$ so that we can also perturb on the other side independently and find an approximation of $v$ in $V$). | |
| Sep 13, 2019 at 23:37 | vote | accept | Trần Quang Minh | ||
| Sep 13, 2019 at 23:34 | history | answered | Jochen Glueck | CC BY-SA 4.0 |