Timeline for Showing integrability of a locally integrable function on a bounded domain under some additional assumptions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14, 2020 at 17:27 | comment | added | Pietro Majer | Excuse me, what result do you mean? | |
| Sep 14, 2020 at 0:17 | comment | added | Ben Ciotti | Ok, so in that case, could the result be shown? Perhaps using the additional assumptions? | |
| Sep 13, 2020 at 8:52 | comment | added | Daniele Tampieri | @BenCiotti, as a matter of fact, substituting $C^1_0(\Omega)$ with $C^1_c(\Omega)$ is equivalent to say that $f$ is a locally integrable function | |
| Sep 13, 2020 at 6:06 | comment | added | Pietro Majer | Isn't this the same as saying $f$ is $ L^1_{loc}(\Omega)$? | |
| Sep 13, 2020 at 0:44 | comment | added | Ben Ciotti | Very nice Pietro, thank you! May I ask a followup (which essentially comes down to the distinction you raised in your first comment)? Suppose I remove the assumption that $fg\in L^1$ for all $g\in C_0^1(\Omega)$, and replace it by the assumption that $fg\in L^1$ for all $g\in C_c^1(\Omega)$. Would the result still hold? Here $C^1_c(\Omega)$ is the set of continuously differentiable functions with compact support in $\Omega$. | |
| Sep 12, 2020 at 23:23 | comment | added | Pietro Majer | Note that no assumption on $\partial\Omega$ are needed | |
| Sep 12, 2020 at 22:31 | history | answered | Pietro Majer | CC BY-SA 4.0 |