Timeline for Fractional-order Rellich–Kondrashov Theorem
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 21, 2023 at 13:29 | comment | added | Hannes | @GuyFsone there is the Frêchet-Kolmogorov(-Riesz) theorem which characterizes compact sets in $L^p$ and whose conditions have a direct connection to certain degrees of smoothness, so this could be a more direct way to go. (A generalization of this theorem is also what is behind the Amann paper the other answer by anonymous and possibly there are some helpful calculations in there.) | |
| Jun 19, 2023 at 7:36 | comment | added | Guy Fsone | @Hannes Are you aware of any other methods, not using interpolation? I am looking for a more direct proof that does not use the compactness of the classical Sobolev $W^1$ into $L^p$. | |
| Jan 14, 2017 at 16:04 | history | edited | Hannes | CC BY-SA 3.0 |
Reference corrected
|
| Jan 14, 2017 at 16:02 | comment | added | Hannes | Whoops, should be Ch. 2.4.1. I'll correct it. | |
| Jan 14, 2017 at 15:56 | vote | accept | anonymous | ||
| Jan 14, 2017 at 15:55 | comment | added | anonymous | (btw, did you really mean to refer to Ch. 2.8.1 in the beginning? I find a series of inclusions there but it seems the interpolation formula one needs is (8) in 2.4.2 on p.185) | |
| Jan 14, 2017 at 15:54 | comment | added | anonymous | Beautiful. I especially like how this can be decomposed into four parts, each with an obvious purpose and comprehensible on its own. To me, the key insight is Theorem 2 from section 1.16.4 that enables the third step. The second step from section 1.2.4 is one that is equally important, but so abstractly stated that I would have overlooked its reach. Thanks! | |
| Jan 14, 2017 at 15:22 | history | answered | Hannes | CC BY-SA 3.0 |