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Results tagged with elliptic-pde
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user 32507
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
1
vote
Seeking references on second-order optimality conditions in $H^1(Ω)$ space
If I understand your comment correctly, you are minimizing over a set
$$
U := \{ u \in H^1(\Omega) \mid a \le u \le b \}
$$
for some $a, b \in L^\infty(\Omega)$.
Such a set is polyhedric in the sense …
- 1,724
6
votes
Accepted
Poincare Inequality for $H^2$ function satisfying homogeneous Robin boundary conditions
This is not true. Take $\Omega = (-1,1)$ and functions $u_M$ like (I hope that I got the constants right)
$$
u_M(x)
=\begin{cases}
-M^2 (|x|-1)(|x|-1+1/M) + M & \text{for } |x| > 1-1/(2M) \\
1/4 + M & …
- 1,724
1
vote
PDE satisfied by projection of a function onto a subspace
This works (only?) for $p = 2$. Let us denote the solution of the PDE on $\Omega$ by $v$.
Then, the variational formulations of the PDEs are
$$\int_D \nabla u \cdot \nabla z - fz \,\mathrm{d}x = 0 \q …
- 1,724