Timeline for Under which conditions does this PDE have unique solutions

7 events

when toggle format	what		by	license	comment
Jun 18, 2022 at 9:23	history	edited	MyShepherd	CC BY-SA 4.0	added 320 characters in body
Jun 18, 2022 at 9:07	history	edited	MyShepherd	CC BY-SA 4.0	added 163 characters in body
Jun 18, 2022 at 8:48	history	edited	MyShepherd	CC BY-SA 4.0	added 35 characters in body
Jun 18, 2022 at 8:42	history	edited	MyShepherd	CC BY-SA 4.0	added 1392 characters in body
Jun 18, 2022 at 8:29	comment	added	MyShepherd		You can impose any constaint on $du$ in order to make the equation elliptic. Demanding it to be a gradient is equivelent to $du=0$. However, you could impose $du=F_{0}$ for any closed vector field $F_{0}$. I will elaborate on this in my answer above.
Jun 17, 2022 at 10:09	comment	added	mlainz		Thank you for your suggestion. As I answered @WillieWong, requiring $u$ to be a gradient is too restrictive. A generalization of this condition is to require $\delta u = g$, that is, $\partial u / \partial x^i - \partial u/ \partial x_j = f_{ii}$, where $f_{ij} = - f_{ji}$. I could then try to study the operator $P$ augmented with the extra equations. Do you know if there in some sense in which this operator could be considered elliptic?
Jun 16, 2022 at 20:10	history	answered	MyShepherd	CC BY-SA 4.0