Timeline for Smallest Lipschitz Constant of a Differentiable Function [closed]
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 13, 2019 at 11:47 | history | closed |
Nik Weaver Piotr Hajlasz abx Alexandre Eremenko Jan-Christoph Schlage-Puchta |
Not suitable for this site | |
| Jan 12, 2019 at 14:47 | vote | accept | emTaMa | ||
| Jan 11, 2019 at 16:01 | answer | added | Nik Weaver | timeline score: 3 | |
| Jan 11, 2019 at 15:59 | comment | added | Nik Weaver | You know what, come to think of it, there's a proof of this in a book I just wrote ... | |
| Jan 11, 2019 at 15:54 | comment | added | Nik Weaver | @StanleySnelson: you have to check the reverse inequality too, which is where convexity comes in: any two points are joined by a line segment and you can apply the one-dimensional mean value theorem. | |
| Jan 11, 2019 at 15:05 | review | Close votes | |||
| Jan 13, 2019 at 11:47 | |||||
| Jan 11, 2019 at 15:00 | comment | added | user126920 | It may be hard to find the proof in a textbook, but you can prove it yourself by taking a point $x$ with $\|\nabla f(x) \|\geq K-\varepsilon$ and finding a $y$ with $|f(y)-f(x)| \geq (K-2\varepsilon)|y-x|$ using the definition of differentiability at $x$. | |
| Jan 11, 2019 at 14:49 | comment | added | Nik Weaver | Undoubtedly this is in Geometric Measure Theory by Federer. But I think this question belongs on math.stackexchange. | |
| Jan 11, 2019 at 14:21 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
MathJax: \sup
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| Jan 11, 2019 at 14:15 | review | First posts | |||
| Jan 11, 2019 at 14:32 | |||||
| Jan 11, 2019 at 14:11 | history | asked | emTaMa | CC BY-SA 4.0 |