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Apr
2
answered Product of Hölder and Sobolev functions
Jan
14
answered Second variation positive definite but not weak local minimum?
Aug
25
comment variational question
The issue with the case $u \not\in H^{2}$ is the integration by parts. In this case the normal derivative along the boundary is not necessarily an element of $H^{1/2}$, but rather one of the dual space $H^{-1/2}$. There are still formulae of integration by parts, but things get tricky (you might loose surjectivity of the trace operator, you have to work with the duality pairings, etc.)
Aug
25
comment equivalence between problem and his variational formulation
Also: first check that your weak formulation is correct, it looks a bit suspicious to me.
Aug
25
answered equivalence between problem and his variational formulation
Aug
25
comment equivalence between problem and his variational formulation
I already helped you a few days ago and you didn't even bother commenting, thanking, accepting or upvoting, but anyway, you have a starting point below as an answer.
Aug
16
answered variational problem -exercice
Aug
16
comment variational problem -exercice
Note that your right hand side $l(v)$ is wrong: the function $g(x)$ is defined on the boundary but you integrate over the whole domain: you should split that integral in two, as you do in the definition of $a(u,v)$.
Feb
21
revised Splitting the action of functionals in duals of Sobolev spaces
added 320 characters in body
Feb
21
comment Splitting the action of functionals in duals of Sobolev spaces
Crossposted (with a delay!) here: mathoverflow.net/questions/122450
Feb
19
awarded  Yearling
Feb
19
answered Why isn't a lemniscate a manifold?
Feb
19
revised Classical solutions of Neumann Laplacian
Relaxing the regularity assumption
Feb
19
comment Application of maximum principle to a function of a complex variable.
You can try to use the fact that both the real and imaginary parts of an holomorphic function are harmonic and therefore only attain their extrema if they are constant.
Feb
19
comment Application of maximum principle to a function of a complex variable.
If I understand it correctly, your calculation is wrong: the absolute value of a function is not differentiable at zero, that is: $\frac{\partial}{\partial z} | \mathfrak{R} ( f) |$ doesn't necessarily exist.
Feb
19
comment Classical solutions of Neumann Laplacian
You are welcome :)
Feb
19
answered Classical solutions of Neumann Laplacian
Feb
19
asked Splitting the action of functionals in duals of Sobolev spaces
Jan
20
answered Meaning of tensor expression
Jan
13
comment Meaning of tensor expression
For matrices this usually means componentwise multiplication.