Timeline for Extension of solutions of PDEs with constant coefficients
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 9, 2015 at 22:40 | vote | accept | BigM | ||
| Dec 8, 2014 at 19:59 | comment | added | Bazin | I should have made my answer more precise, since it deals indeed with real analyticity (I have modified my answer). Of course, ellipticity alone does not imply the sought property globally in $\mathbb C^n$: take for instance for $n=1$, $\frac{\partial}{\partial z}$ and the elliptic equation $\frac{\partial u}{\partial z}=0$, which has no (non-trivial) holomorphic function as a solution. | |
| Dec 8, 2014 at 19:56 | history | edited | Bazin | CC BY-SA 3.0 |
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| Dec 8, 2014 at 15:27 | comment | added | Alexandre Eremenko | Could you give the exact reference on Hormander where he proves that analyticity holds in the WHOLE $C^n$. I only found "in a complex neigborhood" of the real subspace. | |
| Dec 8, 2014 at 13:02 | comment | added | BigM | thanks.I did not know about hypoelliticity at all. Now assuming the operator is elliptic should we expect that solutions extend to entire functions?entirety is of course much stronger than analyticity. | |
| Dec 8, 2014 at 12:02 | history | answered | Bazin | CC BY-SA 3.0 |