Timeline for Convergence of elliptic operators
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 3, 2011 at 21:44 | comment | added | Deane Yang | Agreed with comments above by Willie and Chris. The only thing required here is the existence of a right inverse $A_0^{-1}$ that recovers all the regularity lost by the differential operator $A_0$. There is a more general class of differential operators known as hypoelliptic operators for which such inverses exist. | |
| Aug 3, 2011 at 21:27 | comment | added | Willie Wong | Ellipticity is only used in so far as $A_0$ is invertible (and if $A_0$ is elliptic, and $A_t\to A_0$ in coefficients as $t\to 0$, $A_t$ is also elliptic for sufficiently small $t$. | |
| Aug 3, 2011 at 20:57 | vote | accept | Chris Judge | ||
| Aug 3, 2011 at 20:57 | comment | added | Chris Judge | I guess ellipticity has nothing to with it. [ \int |(A-B) u|^2 \leq C \sum_{\alpha} \int |\partial^{\alpha} u|^2] where [ C= \sup |a_{\alpha}- b_{\alpha}|^2] where $\alpha$ is a multi-index and the $a$'s and $b$'s are the coefficients. | |
| Aug 3, 2011 at 20:36 | comment | added | Chris Judge | Is ellipticity necessary? (Part of the `why' part of question...) | |
| Aug 3, 2011 at 17:32 | history | answered | Deane Yang | CC BY-SA 3.0 |