Timeline for Harmonic functions in infinite domain in Euclidean space
Current License: CC BY-SA 4.0
12 events
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| Sep 11, 2021 at 16:57 | vote | accept | asv | ||
| Sep 11, 2021 at 16:02 | review | Close votes | |||
| Sep 21, 2021 at 3:03 | |||||
| Sep 11, 2021 at 15:40 | comment | added | Alexandre Eremenko | Any harmonic function which vanishes on $\partial\Omega$ AND at $\infty$ is evidently zero. This follows from the Maximum Principle. | |
| Sep 11, 2021 at 14:55 | history | edited | Willie Wong |
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| Sep 11, 2021 at 14:53 | answer | added | Willie Wong | timeline score: 2 | |
| Sep 11, 2021 at 14:20 | history | edited | asv | CC BY-SA 4.0 |
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| Sep 11, 2021 at 14:13 | comment | added | asv | @WillieWong: You are right, thanks. I edited the question. | |
| Sep 11, 2021 at 14:12 | history | edited | asv | CC BY-SA 4.0 |
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| Sep 11, 2021 at 14:06 | comment | added | Willie Wong | Without boundary conditions there is no rate that suffice. In $n = 3$ for example $\partial_1^m \frac1r$ is harmonic and decays like $r^{-1-m}$. | |
| Sep 11, 2021 at 14:04 | comment | added | asv | @MichaelEngelhardt: well, there is a bounded smooth domain containing the ball, such that on its boundary the function vanishes. | |
| Sep 11, 2021 at 13:40 | comment | added | Michael Engelhardt | You'd at least have to say something about the boundary conditions on the surface of the ball ... | |
| Sep 11, 2021 at 12:47 | history | asked | asv | CC BY-SA 4.0 |