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Jun 15, 2020 at 7:27 history edited CommunityBot
Commonmark migration
Jan 11, 2016 at 14:07 review Close votes
Jan 12, 2016 at 0:14
Jan 11, 2016 at 13:51 comment added Deane Yang Thomas's remark, along with the definitions of the two spaces you're trying to decide between, immediately gives the answer. This is more appropriate for math.stackexchange.com
Jan 11, 2016 at 10:30 comment added Thomas Richard Maybe you already know that, but by integration by parts your norm is equal to $\left(\int_\Omega|D^2u|^2dx\right)^{1/2}$ since $\langle \nabla u,\nabla\Delta u\rangle=-|D^2u|^2+\tfrac{1}{2}\Delta|\nabla u|^2$ where $|D^2u|^2$ is the Frobenius norm of the Hessian.
Jan 11, 2016 at 3:56 comment added Nate Eldredge I don't see how it can possibly be $W^{2,2}_0(\Omega)$. For instance, the completion certainly can't contain any function whose Laplacian isn't radially symmetric.
Jan 11, 2016 at 0:54 history asked Hheepp CC BY-SA 3.0