Timeline for Aleksandrov maximum principle for semi-convex function
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2020 at 17:11 | comment | added | Giovanni Febbraro | Yes, I have to proof the statement for less regular $u$. The goal is to find the statement as lower as possible regularity of $u$. This can be done through the semiconvex function. | |
| Mar 17, 2020 at 16:45 | comment | added | Giorgio Metafune | Still I do not undestand your answer. For $C^2$ functions we agree that Alexandrof maximum principle holds. Then the question is meaningful for less regular $u$ (or $z$, which is the same). Did I understand correctly or convexity palys other roles? | |
| Mar 17, 2020 at 16:18 | comment | added | Giovanni Febbraro | No, I don't think. | |
| Mar 17, 2020 at 16:05 | answer | added | Connor Mooney | timeline score: 4 | |
| Mar 17, 2020 at 15:23 | comment | added | Giorgio Metafune | So the question is about the regularity of $u$; for example $u$ could be just a convex function? | |
| Mar 17, 2020 at 14:52 | comment | added | Giovanni Febbraro | @GiorgioMetafune I know proofs of Aleksandrov principle when the function $u$ has some useful regularity, as $C^2$ or $W^{2,n}$. In my question all these regularity are not assumed. The only think you know is that $u$ is semiconvex and this implie that $u$ is twice differentiable a.e.. You know some proofs that not use the regularity? | |
| Mar 17, 2020 at 14:41 | comment | added | Giorgio Metafune | Sorry, I do not understand. The usual Alexandrov principle holds without any convexity assumption on $u$. What is the question? | |
| S Mar 17, 2020 at 11:37 | history | suggested | Daniele Tampieri | CC BY-SA 4.0 |
Formatting, minor Math Jaxing + typos and grammar
|
| Mar 17, 2020 at 9:52 | review | Suggested edits | |||
| S Mar 17, 2020 at 11:37 | |||||
| Mar 17, 2020 at 8:55 | review | First posts | |||
| Mar 17, 2020 at 9:13 | |||||
| Mar 17, 2020 at 8:52 | history | asked | Giovanni Febbraro | CC BY-SA 4.0 |