Timeline for Harmonic level sets and boundary data
Current License: CC BY-SA 2.5
13 events
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| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://dl.dropbox.com/ with https://dl.dropbox.com/
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| Apr 9, 2013 at 14:49 | answer | added | Loïc Teyssier | timeline score: 2 | |
| Nov 21, 2010 at 4:51 | answer | added | partition_of_unity | timeline score: 3 | |
| Nov 21, 2010 at 4:48 | history | edited | partition_of_unity | CC BY-SA 2.5 |
Moving update into an answer to not lose the original question
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| Nov 21, 2010 at 3:08 | history | edited | partition_of_unity | CC BY-SA 2.5 |
Highlighted the main questions.
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| Nov 21, 2010 at 3:00 | history | edited | partition_of_unity | CC BY-SA 2.5 |
added images and enhanced the question.
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| Nov 19, 2010 at 20:45 | answer | added | Willie Wong | timeline score: 5 | |
| Nov 12, 2010 at 22:36 | comment | added | Will Jagy | Let $\theta$ be the angle around the boundary, from $0$ to $2 \pi$ as usual. Let your boundary function be $f(\theta) = \sin ( 3 \theta)$ and make a new graphic, and make sure that one of the level sets depicted is $ u_f = 0.$ | |
| Nov 12, 2010 at 12:50 | comment | added | partition_of_unity | That's really interesting, is there a theorem that explains this? Is there a way to choose the boundary data in such a way to make the level sets not arcs? maybe to make the boundaries of the level sets to be only a Lipschitz curve? | |
| Nov 12, 2010 at 3:40 | history | edited | partition_of_unity |
Added tag
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| Nov 12, 2010 at 3:00 | comment | added | Will Jagy | The thing to concentrate on is that in the interior, connected components of level sets of a harmonic function are either nice arcs, as your graphic shows, or like the zero set of the imaginary part of $$ ( x + i y)^n $$ for integer $ n \geq 2.$ If you picked exactly the right level in your graphic you could see such a point where multiple arcs intersect. | |
| Nov 12, 2010 at 2:21 | history | edited | partition_of_unity | CC BY-SA 2.5 |
Added image, sorry can't seem to embed.
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| Nov 12, 2010 at 1:26 | history | asked | partition_of_unity | CC BY-SA 2.5 |