Timeline for Does elliptic regularity guarantee analytic solutions?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 22, 2011 at 1:16 | comment | added | Rbega | As for a geometric application...While analyticity itself is not so important, one of its consequences is. Namely, the fact that two distinct solutions to some (non-linear) elliptic equation (of an appropriate form) can only agree at a point to finite order. This unique continuation property--which is strictly weaker than analyticity--actually holds for quite a general class of elliptic equations. This comes up, for instance, in the regularity theory for minimal surfaces--specifically in analyzing branch points of minimal surfaces. | |
| Jun 22, 2011 at 0:55 | comment | added | Rbega | I'm curious about how you propose to show regularity properties of holomorphic functions without appealing to some form of elliptic regularity... | |
| Jun 21, 2011 at 21:52 | answer | added | Viktor Bundle | timeline score: 7 | |
| Aug 11, 2010 at 17:34 | vote | accept | Paul Siegel | ||
| Jul 28, 2010 at 12:52 | comment | added | Hans Lundmark | Rudin's book, that is. :) Example 8.14, to be precise. | |
| Jul 28, 2010 at 5:57 | comment | added | Mariano Suárez-Álvarez | Rubin' s book on functional analysis, that is. | |
| Jul 28, 2010 at 5:43 | comment | added | Mariano Suárez-Álvarez | The example of holomorphic functions (in fact, the statement that an hoomorphic distribution is in fact a smooth function) is given in RUbin's book as an example. | |
| Jul 28, 2010 at 5:31 | answer | added | Mariano Suárez-Álvarez | timeline score: 12 | |
| Jul 28, 2010 at 4:40 | answer | added | Torsten Ekedahl | timeline score: 7 | |
| Jul 28, 2010 at 4:21 | history | asked | Paul Siegel | CC BY-SA 2.5 |