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gerw
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answered
Typo in error a-priori estimate in a discontinuous Galerkin paper?
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Minimiser of a certain functional
$L^1(0,1)$ is not a dual space. How do you define weak-* convergence?
answered
Decomposition of non negative Radon measure into $L^1$ and $H^{-1}$ functions
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Decomposition of non negative Radon measure into $L^1$ and $H^{-1}$ functions
Can you point to some work where this result is used? Are the three decomposed parts again non-negative?
comment
$H_0^1(\Omega, D) \hookrightarrow L^2(D)$ is compact, for $\Omega$ quasi-open in $D$ - Proof verification
Oh, sorry, I missed that $D$ might fail to be bounded. But then, the keyword might be "uniformly Lipschitz". However, there no definition of this term appears in the paper.
answered
$H_0^1(\Omega, D) \hookrightarrow L^2(D)$ is compact, for $\Omega$ quasi-open in $D$ - Proof verification
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How do you call a linear programming problem when the solution should be "constrained" to a norm?
$Ca = d$ is equivalent to "$C a \le d$ and $Ca \ge d$".
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How do you call a linear programming problem when the solution should be "constrained" to a norm?
Yes, you encode these conditions via a linear system of equations.
answered
When is a convex function continuous on its domain?
answered
How do you call a linear programming problem when the solution should be "constrained" to a norm?
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Poincare Inequality for $H^2$ function satisfying homogeneous Robin boundary conditions
@Fozz: Yes, this is possible.
awarded
 Yearling
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Poincare Inequality for $H^2$ function satisfying homogeneous Robin boundary conditions
Yes, if I did not introduce an error, $u_M$ should belong to $C^{1,1} = W^{2,\infty}$.
answered
Poincare Inequality for $H^2$ function satisfying homogeneous Robin boundary conditions
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When is a function a convex conjugate?
I don't think that this is true (unless $X$ is reflexive). The conjugate of the preconjugate is always weak-* lower semicontinuous. Hence, you have to assume at least that $g$ is weak-* lower semicontinuous.
awarded
 Constituent
awarded
 Caucus
answered
Measurability of essential supremum of function of two variables
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Sobolev embedding if $p=3/2$, $n=3$ and $k=2$
My answer is still valid.
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Sobolev embedding if $p=3/2$, $n=3$ and $k=2$
I am confused. To get $0$ on the lhs, we need (for $n = 3$ and $k = 2$) $p = 3/2$. And then, $W^{2,3/2} \subset W^{1,3} \subset BMO$.
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