Timeline for Meaning of Alberti rank-one theorem
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 17, 2019 at 11:58 | comment | added | Bazin | Let me put it that way. You must try to prove your theorem on your vector field $X$ (say uniqueness of weak solutions) for the particular case where $DX$ is as above, which is not so easy. After this, you enter a more technical area, in which you are not stricto sensu reduced to that case, but you can argue via an approximation procedure. The key argument for the uniqueness of weak solutions is a commutator estimate between the vector field and a smoothing operator, and this argument leaves plenty of room for approximation. | |
| Apr 16, 2019 at 11:50 | comment | added | user123457 | After going through your reference, I'm still unclear about the fact that "through an approximation procedure, you may indeed assume that singularity occurs by differentiating only in one direction (and with null divergence (or ac) is concerning only one off-diagonal coefficient).". Could you add some details on it? | |
| Apr 11, 2019 at 18:45 | vote | accept | CommunityBot | ||
| Dec 12, 2018 at 14:14 | comment | added | Bazin | I have no more heuristic explanations. If you want to enter the details, I would recommend the paper MR2124585,Transport equations with partially BV velocities, by N. Lerner and the L. Ambrosio article quoted there. | |
| Dec 11, 2018 at 21:54 | history | edited | Bazin | CC BY-SA 4.0 |
Some more comments.
|
| Nov 23, 2018 at 22:22 | history | answered | Bazin | CC BY-SA 4.0 |