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Results tagged with ap.analysis-of-pdes
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user 40644
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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 …
5
votes
1
answer
355
views
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 …