Timeline for Existence of a special function
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 24, 2020 at 8:38 | comment | added | LSpice | You ask for a smooth function that vanishes in a certain range, with (as you say) no other condition. Why doesn't $f = 0$ satisfy that? | |
| Jun 23, 2020 at 13:45 | comment | added | MathGeo | No. Note that I removed the second condition. | |
| Jun 23, 2020 at 6:23 | comment | added | Ben McKay | Does $f=0$ satisfy your conditions? | |
| Jun 21, 2020 at 20:18 | vote | accept | MathGeo | ||
| Jun 21, 2020 at 19:07 | answer | added | Bazin | timeline score: 3 | |
| Jun 21, 2020 at 17:29 | history | edited | MathGeo | CC BY-SA 4.0 |
Modify the question accordingly to get some ideas.
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| Jun 21, 2020 at 15:55 | comment | added | MathGeo | You're right. I think I should at least modify the second condition. Now, I consider just the first one. | |
| Jun 21, 2020 at 15:39 | comment | added | LSpice | According to your requirements, unless I am misreading, $b = f^{-1}(0) \cap \partial D$ and $\partial D \setminus b = f^{-1}(1) \cap \partial D$, both of which are closed in $\partial D$. | |
| Jun 21, 2020 at 15:37 | comment | added | MathGeo | @Lspice I don't see why it must be open and closed. I can assume it to be open w.r.t $\partial D$. The same value on whole domain is not what I need. | |
| Jun 21, 2020 at 15:15 | review | Close votes | |||
| Jun 26, 2020 at 9:11 | |||||
| Jun 21, 2020 at 14:53 | comment | added | LSpice | Such a $b$ must be both open and closed in the boundary, so be a union of components. If the boundary is connected, that means that you ask $f$ to be $0$ or $1$ on all of $\partial D$, so you may just take it to have that same value on all of $\overline D$. | |
| Jun 21, 2020 at 14:42 | history | asked | MathGeo | CC BY-SA 4.0 |