Timeline for fractional compact Sobolev embedding on lipschitz domain
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2019 at 18:17 | comment | added | mathyul | Great. The multiplicative/interpolation inequality is quite instructive. In fact, I found related theorems from page 26, "Elliptic problems in nonsmooth domains" by Pierre Grisvard. | |
| Jul 18, 2019 at 7:42 | comment | added | Hannes | See this related question. (Note that the $W^{s,2}$ and the $H^s$ scale coincide, on $R^n$ in general and on $\Omega$ because of your supposed Lipschitz regularity.) Essentially, you want to obtain a multiplicative inequality $\|u\|_{H^\delta(\Omega)} \leq C \|u\|_{L^2(\Omega)}^{1-\delta} \|u\|_{H^1(\Omega)}^\delta$, from which your desired compactness follows via Rellich-Kondrachov. | |
| Jul 18, 2019 at 5:00 | review | First posts | |||
| Jul 18, 2019 at 8:00 | |||||
| Jul 18, 2019 at 4:55 | history | asked | mathyul | CC BY-SA 4.0 |