Timeline for Is the Lipschitz constant of $f$ equal to $\|\nabla f\|_{L^\infty}$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2023 at 16:31 | comment | added | Mikhail Katz | You may want to check out the reference at wiki where it is stated that "any Lipschitz function on Ω is an element of the space W1,∞(Ω)". The reference is to Evans and Gariepy. | |
| Jul 25, 2023 at 16:31 | vote | accept | Akira | ||
| Jul 25, 2023 at 16:27 | answer | added | Nik Weaver | timeline score: 4 | |
| Jul 25, 2023 at 16:06 | comment | added | Akira | @ThomasKojar From your link, I get that $\|\nabla f\|_{L^\infty} \le [f]$. For the reverse inequality, Julien's proof (in Question 2.2) requires that $f$ is differentiable everywhere. | |
| Jul 25, 2023 at 15:45 | history | asked | Akira | CC BY-SA 4.0 |