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Results tagged with sobolev-spaces
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user 40644
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
1
vote
Trace spaces on convex polyhedra: compatibility conditions at edges
I do not own the book but you might find something in Mazya's and Rossmann's Elliptic Equations in Polyhedral Domains. Hope this might help...
2
votes
Accepted
Elliptic pde with bilaplacian; boundary conditions.
You will not get a direct variational structure (because of the boundary conditions) but there is a mixed approach that will work on your case: Set $-\Delta u=v$ and obtain the following system:
$$
\b …
1
vote
Can you pair $H^s(\Omega)$ and $H^{-s}(\Omega)$ on a domain $\Omega$?
You could, by extension, if your domain has a boundary that is at least Lipschitz, but the analysis could become quite tricky. Take a look at Gerd Grubb's book: Functional Calculus of Pseudodifferenti …
1
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$\lVert u\rVert_{W^{2,p}}$ is bounded above by $\lVert \Delta_p u\rVert_{L^2}$ for $u \in W^...
You could take a look at Chapter 3 of P. Lindqvist's notes:
http://www.math.ntnu.no/~lqvist/p-laplace.pdf
Since you work in a bounded domain there is also the matter of boundary regularity. Even for …