Timeline for partial maximum principle for elliptic differential operators
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 5, 2013 at 14:39 | comment | added | Viktor Bundle | Willie Wong: No, I don't require that $P$ is second-order. I'm particularly interested in the fourth-order case. | |
| Jul 4, 2013 at 12:15 | comment | added | Willie Wong | (I meant to write $P = (\triangle + k)^2$, of course. But one can obviously also just look at $(\triangle)^2 + k^2$ for which the argument is even simpler...) | |
| Jul 4, 2013 at 12:13 | review | Close votes | |||
| Jul 6, 2013 at 5:31 | |||||
| Jul 4, 2013 at 12:03 | comment | added | Willie Wong | Do you want to require $P$ to be second order? Otherwise I don't see why your claim (the existence of a maximal principle) has to be true. Simply take $P = (\triangle)^2 + k^2$, it is clearly self-adjoint and elliptic, and $\langle Pu,u\rangle = \langle \triangle u + ku,\triangle u + ku\rangle > 0$ provided $k$ is chosen so that $\triangle u + ku = 0$ has no solutions. For this $P$ you have that the function $u = 1$ satisfies $u > 0$ and $Pu = u > 0$. | |
| Jul 4, 2013 at 11:39 | history | asked | Viktor Bundle | CC BY-SA 3.0 |