Timeline for Interpolation spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 11, 2020 at 9:54 | comment | added | Hannes | @Kore-N sure, see for instance Chapter 4 in Interpolation Theory by Alessandra Lunardi. (Or Chapter 1.15.3 in the Triebel book.) | |
| Nov 25, 2020 at 14:44 | comment | added | Kore-N | @Hannes do you have a reference for your "general formula"? In particular one that holds for a large class of operators, not just the laplacian? | |
| Sep 7, 2017 at 20:35 | comment | added | Sebastian Bechtel | Even for mixed boundary conditions and suitable non-smooth bounded domains one gets $\operatorname{dom}(-\Delta)^{s/2}=H^s_D(\Omega)$ for some $s$ slightly above $1$, where the Laplacian is subject to mixed boundary conditions and the Bessel potential space embodies those boundary conditions as well. | |
| Sep 7, 2017 at 14:45 | comment | added | Mateusz Kwaśnicki | Just wondering: what can one tell about $\operatorname{dom}(-\Delta_D)^{s/2}$ for $s>1$? Is it always $H^s(\Omega) \cap H^1_0(\Omega)$? This seems to be true when $1<s<2$, but what about $s>2$? | |
| Sep 7, 2017 at 14:45 | comment | added | Thomas | Thank you very much. Do we also have that $\left [H^m(\Omega) \cap H_0^1(\Omega) , L^2(\Omega)\right ]_{1-\frac s m}=\text{dom}(-\Delta_D)^{\frac s 2}$? | |
| Sep 7, 2017 at 14:39 | history | answered | Hannes | CC BY-SA 3.0 |