Timeline for Equivalence of Sobolev spaces for different metrics
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2019 at 17:26 | comment | added | Deane Yang | You could do this without using local coordinates. However, since you'll need to integrate by parts and permute the covariant derivatives, lower order terms involving the curvature and its covariant derivatives will appear. The proof is more or less just as messy as using local coordinates. | |
| Apr 3, 2019 at 12:27 | comment | added | Deane Yang | It suffices to do it in local coordinates. | |
| Mar 5, 2019 at 9:29 | comment | added | Δημήτρης Ο | This works in the second order case (after providing a bit of detail). But I was asking for an approach that would cover every case and would not depend on expressions of local coordinates. | |
| Mar 4, 2019 at 3:19 | history | answered | Ryan Unger | CC BY-SA 4.0 |