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Results tagged with elliptic-pde
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user 40644
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
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 …
5
votes
1
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Regularity up to the boundary for the Poisson problem
It seems that the following assertion is widely accepted:
For $k\in\mathbb N$, $p\geq 2$, $\Omega \subset \mathbb R^n$ bounded with $\partial\Omega\in C^{k+2}$ and $f\in W^{k,p}(\Omega)$, the weak so …