Timeline for Existence of a special function
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2020 at 15:38 | comment | added | Bazin | Well, near every point of the boundary, you have a local function $\rho$, so that you can cover the boundary by a finite collection of open sets $\{U_k\}_{1\le k\le N}$ to which you add $U_0=\Omega$. Using a partition of unity (see e.g. Section 1.4 in Hörmander's ALPDO I) you can construct a global $\rho$. | |
| Jul 10, 2020 at 1:36 | comment | added | S. Maths | @Bazin could you provide a reference to a proof of the existence of such $\rho$? Thanks. | |
| Jun 22, 2020 at 22:44 | comment | added | Bazin | Partition of unity. | |
| Jun 22, 2020 at 4:03 | comment | added | LSpice | Why can your locally defined function be pieced together to a global function? | |
| Jun 21, 2020 at 21:58 | comment | added | Bazin | That removed condition would make the smoothness impossible: the most caricatural case would be the situation where $b$ is reduced to a single point of the boundary. | |
| Jun 21, 2020 at 20:20 | comment | added | MathGeo | Thank you. Could you give your opinion about the condition I removed, If we can get something close? | |
| Jun 21, 2020 at 20:18 | vote | accept | MathGeo | ||
| Jun 21, 2020 at 19:07 | history | answered | Bazin | CC BY-SA 4.0 |