Timeline for When is a Nemytskii map between Sobolev spaces compact?
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| May 26, 2017 at 10:20 | vote | accept | GuestUser | ||
| May 3, 2017 at 11:33 | comment | added | Pietro Majer | For the non-compactness of the set $E$: start with a sequence $u_j\in H^1$ with $\|\nabla u_j\|_2=1$ and $u_j \to 0$ a.e. If $f(t):=\mathrm{dist}(t,\mathbb{Z})$, then $v_j:=f(u_j)$ has still $\|\nabla v_j\|_2=1$, $v_j \to 0$ a.e. and also $\|v_j\|_{\infty}\le1$. | |
| May 3, 2017 at 11:02 | history | answered | Pietro Majer | CC BY-SA 3.0 |