Timeline for Implicit function theorem when $dF/dy = 0$ but under monotonicity constraint of the implicit function $y(x)$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2021 at 9:48 | comment | added | G. Ander | The implicit function theorem does not apply when $\partial f / \partial y = 0$. But, as in the two examples I'm giving here, if I know that I'm looking for a strictly increasing "implicit function", then uniqueness still holds (provided $\partial f / \partial y$ is not flat). However, I'm showing it without resorting to differential equations, implicit differentiation or a variant of the implicit function theorem; So I would like to find a way to prove it using these tools (as my version of the proof does not generalize easily to higher dimension/more general problems). | |
| Oct 29, 2021 at 9:31 | comment | added | Dieter Kadelka | For me its no clear what is your problem. A function $F \colon \mathbb{R}^n \to \mathbb{R}$, $F \in C^1$ is given. I think $n = 2$. You want to show exactly what? | |
| Oct 29, 2021 at 8:43 | history | asked | G. Ander | CC BY-SA 4.0 |