Timeline for Extension of harmonic function
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 12, 2021 at 14:47 | comment | added | Jiaze Zhang | Schwartz refers to the mathematician Laurent Schwartz; the Schwartz space of functions is named after him. Schwarz refers to Hermann Schwarz; the Schwarz reflection principle is named after him. | |
| Jul 6, 2012 at 23:57 | comment | added | Slm2004 | I am not sure your are right. As I said, I don't have a rigorous proof of the analytic case. My point is we can use adapted Schwartz reflection principle to extend u. The harmonic conjugate of u were not necessary to be constant. Suppose $\Omega$ is simply connected domain, then u is real part of holomorphic function $f$. We can always extend $f$ respect to an analytic curve. So we can extend $u$ | |
| Jul 6, 2012 at 23:44 | vote | accept | Slm2004 | ||
| Jul 6, 2012 at 21:33 | comment | added | John Pardon | The Schwartz reflection principle would only work if the harmonic conjugate of $u$ were constant along that particular arc on $\partial\Omega$ (or equivalently, if the normal derivative of $u$ vanishes there). | |
| Jul 6, 2012 at 16:59 | answer | added | Pietro Majer | timeline score: 8 | |
| Jul 6, 2012 at 15:30 | history | edited | Slm2004 | CC BY-SA 3.0 |
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| Jul 6, 2012 at 15:18 | history | edited | Slm2004 | CC BY-SA 3.0 |
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| Jul 6, 2012 at 15:12 | history | asked | Slm2004 | CC BY-SA 3.0 |