Timeline for Trace of a function
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 25, 2021 at 15:36 | comment | added | Hannes | I guess all the vector valued stuff is not enough as long as one needs $H^s(0,L)$ with $s>1/2$ for the trace; even if we could interpolate the vector-valued function spaces in an optimal way, the obstruction $s>1/2$ will still produce the $4-\varepsilon$. | |
| Jan 25, 2021 at 15:19 | comment | added | Willie Wong | Please do! I don't have a copy of Lions--Magenes and would love to know if there's a strengthening. (But yes, I entirely agree that vector valued interpolation with differentiability index is a big can of worms. Didn't B&L deliberately omit all but the simplest cases?) | |
| Jan 25, 2021 at 15:13 | comment | added | Hannes | You are right, it is not really necessary. I did try to rely on the "best known" results and not open the can of worms of vector-valued interpolation in the differentiability index (and embeddings). I thought one did not lose anything there since the $\varepsilon$ missing at the end would occur anyway, but I just realized that seemingly may not occur in the Hilbert space case according to the Lions/Magenes book. I will check further. | |
| Jan 25, 2021 at 14:47 | comment | added | Willie Wong | My interpolation theory is a bit rusty and my copy of B&L is in my office: is it necessary to go through the intermediate interpolation for $X\hookrightarrow C([0,T]; L^2)$? Can one not directly take the complex interpolant of $[L^2_t H^1_x, H^1_t H^{-1}_x]_s$? | |
| Jan 25, 2021 at 12:26 | history | answered | Hannes | CC BY-SA 4.0 |