Timeline for Unusual problem of calculus-of-variations
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2018 at 20:26 | comment | added | Carlo Beenakker | update at mathoverflow.net/q/296566/11260 | |
| Mar 22, 2018 at 11:39 | comment | added | Ben McKay | The maximum principle tells us that $u$ is everywhere zero, as both $u$ and $-u$ are harmonic, so achieve their maxima on the boundary, as Michael Renardy says. | |
| S Mar 22, 2018 at 4:40 | history | suggested | David G. Stork | CC BY-SA 3.0 |
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| Mar 21, 2018 at 23:20 | review | Suggested edits | |||
| S Mar 22, 2018 at 4:40 | |||||
| Mar 21, 2018 at 17:15 | comment | added | fedja | Peter, have you paid attention to what Michael said? The only harmonic $u$ that satisfies the Dirichlet boundary condition you imposed is identically $0$, so editing the normalization condition won't help much: the problem is just nonsensical as posed. Perhaps, you meant something else (say no boundary condition, just the normalization itself). | |
| Mar 21, 2018 at 17:12 | comment | added | Peter | I made a typo. It should be $\int u^2(x,y)dxdy=1$. It is a usual normalization, which is fix a constant. | |
| Mar 21, 2018 at 17:09 | history | edited | Peter | CC BY-SA 3.0 |
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| Mar 21, 2018 at 15:26 | comment | added | Michael Renardy | Aren't solutions of the Dirichlet problem unique? How can the integral of u be 1? | |
| Mar 21, 2018 at 13:06 | comment | added | Dirk | I guess the buzz word is "free boundary problem" | |
| Mar 21, 2018 at 11:59 | history | edited | Peter | CC BY-SA 3.0 |
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| Mar 21, 2018 at 11:24 | review | First posts | |||
| Mar 21, 2018 at 11:29 | |||||
| Mar 21, 2018 at 11:21 | history | asked | Peter | CC BY-SA 3.0 |