Timeline for Does the pointwise mean value property imply harmonicity?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| 2 days ago | comment | added | No-one | The result by Volterra can be found in his paper "Alcune osservazioni sopra proprietà atte ad individuare una funzione". | |
| Oct 27, 2021 at 3:41 | history | edited | LSpice | CC BY-SA 4.0 |
`\eqref`
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| Oct 27, 2021 at 0:04 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 5 characters in body; edited title
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| Oct 25, 2021 at 21:17 | history | became hot network question | |||
| Oct 25, 2021 at 19:57 | comment | added | Willie Wong | For those who don't want to click through: @ViníciusNovelli linked to Llorente's 2015 paper in CPAA, which includes a broad survey of related results. In addition to the positive theorem of Volterra and Kellogg, it is also mentioned that boundedness of $u$ and boundedness of $\Omega$ are important, and dropping either can lead to counterexamples, and that the various cases (positive and negative) are treated by Hansen and Nadirashvili (as mentioned in the answer below). | |
| Oct 25, 2021 at 15:20 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Oct 25, 2021 at 14:53 | answer | added | Alexandre Eremenko | timeline score: 8 | |
| Oct 25, 2021 at 13:35 | comment | added | Vinícius Novelli | If $\Omega$ is bounded and $u\in C(\overline{\Omega})$, then the answer is yes, it is harmonic. This is a result of Volterra and Kellogg, check theorem $2.1.3$ in this paper | |
| Oct 25, 2021 at 13:17 | history | asked | Guy Fsone | CC BY-SA 4.0 |