Timeline for Analyticity of the solutions of PDE
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2013 at 19:19 | comment | added | timur | Rafe, I thought that the heat operator is not analytic hypoelliptic, even though it is Gevrey hypoelliptic. It might be analytic hypoelliptic in certain directions though. | |
| Apr 20, 2013 at 19:17 | comment | added | timur | @Otis: For constant coefficient operators, Petrowsky proved that analytic hypoellipticity is equivalent to ellipticity of the symbol. He also proved that elliptic operators with analytic coefficients are analytic hypoelliptic. | |
| Aug 16, 2012 at 19:19 | comment | added | Otis Chodosh | Rafe, can you detect analytic hypoellipticity via the symbol? (Am I mistaken in remembering that you can detect hypoellipticity via the symbol?) Cool answer, thanks! | |
| Aug 16, 2012 at 15:58 | comment | added | Rafe Mazzeo | My apologies then. | |
| Aug 16, 2012 at 7:03 | vote | accept | Cristi Stoica | ||
| Aug 16, 2012 at 6:48 | comment | added | Cristi Stoica | Thanks for the answer. On the other hand, while I agree that Otis's attempt was sincere, I disagree that my reply was rude at all, and I even don't see what may have appeared to you impolite in what I wrote. I tried to explain better what I need, and what I need differs from particularizing the problem and risking, by adding conditions, to miss what I am interested in, and making the problem too localized. | |
| Aug 16, 2012 at 2:02 | comment | added | Deane Yang | Rafe, thanks for a much better answer than mine, especially the example of $\partial_1$. | |
| Aug 16, 2012 at 0:02 | history | answered | Rafe Mazzeo | CC BY-SA 3.0 |