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A function $u:[a,b] \to \mathbb R$ is Lipschitz if and only if $u \in W^{1,\infty}([a,b])$.

Is it also true for $u:\Omega \to \mathbb R$ for $\Omega \subseteq \mathbb R^n$?

user35319
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  • https://en.wikipedia.org/wiki/Sobolev_space#Other_examples would suggest otherwise? – copper.hat Jun 21 '20 at 06:43
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    If $\Omega$ is sufficiently nice, it is true. See this question https://math.stackexchange.com/questions/269526/sobolev-embedding-for-w1-infty – Winger 14 Jun 21 '20 at 19:17

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