How does function $x_i \rightarrow f(x_1,x_2, ..., x_i, ..., x_n)$ Lipschitz imply existence of partial derivatives?

Question

Particularly, is there a way to write this in such form that expresses component-wise differentiability?

Lipschitz functions are not necessarily everywhere differentiable: https://en.wikipedia.org/wiki/Lipschitz_continuity#Examples — edm, Oct 25 '19 at 02:18
@edm But actually in my case "almost everywhere differentiable" suffices. — mavavilj, Oct 25 '19 at 02:18

score 0 · Answer 1 · answered Oct 25 '19 at 02:25

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This question will help you: Lipschitz continuity implies differentiability almost everywhere. This problem is a little bit hard to solve, but there is a reference in this question with the prove.

answered Oct 25 '19 at 02:25

ABP

I was reading that paper, it doesn't explain it fully. Only in broad strokes. – mavavilj Oct 25 '19 at 02:33

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