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17h
comment How many minimally sides are needed to fully enclose a volume in an $n$-dimensional spaece?
It sound like the OP is paying per plate and not per area. Nethertheless a very nice answer!
17h
answered Questions of an example of a measurable function fails to be continuous everywhere or even, almost everywhere
1d
comment polyhedral function
Do you know how to get the epigraph of a sum/max of functions in terms of their epigraphs?
1d
answered The dual function of composite functions
2d
comment The dual function of composite functions
In case $K$ being invertible, you get $(F\circ K)^*(x^*) = F^*(K^{-*}(x^*))$.
2d
comment The dual function of composite functions
Do you mean $(F \circ K)^*(x)$?
2d
comment The space $\{ u \in H^1(\Omega) \mid \Delta u \in L^2(\Omega)\}$
But the Laplacian is also defined in a weak sense, so it perfectly fits together.
2d
revised The space $\{ u \in H^1(\Omega) \mid \Delta u \in L^2(\Omega)\}$
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Jul
23
comment Uniform Boundedness: Nets
I do not understand (the notation of) the first question. Concerning the second question: the proof of this fact for sequences which I know, utilizes that the convergence $T_\lambda x \to Tx$ implies boundedness of $T_\lambda x$ (w.r.t. $\lambda$) which might not hold for nets. A counterexample could be the following: take a unbounded net of functionals $f_\lambda \in X^*$ which converges to $f$. Then, $f_\lambda(x) \to f(x)$, but $f_\lambda(x)$ cannot be bounded w.r.t. $\lambda$ (for all $x$), since this would imply (by the uniform boundedness principle) the boundedness of $f_\lambda$.
Jul
23
answered Uniform Boundedness: Nets
Jul
22
answered Existence of unique solution in Banach space
Jul
22
comment Linear like functions
This is not functional analysis.
Jul
22
revised Linear like functions
edited tags
Jul
22
answered Limit inferior, weak convergence
Jul
21
answered The intersection of $BV$ space.
Jul
16
comment Sobolev functions counterexample
@Pedro: See the edit. Actually, it is not a characterization of $H_0^2$.
Jul
16
revised Sobolev functions counterexample
added 557 characters in body
Jul
15
comment Is it incorrect to say that a functional “maps functions to numbers”?
@user251257: I think I misunderstood the last sentence in the question.. Sorry!
Jul
15
comment Is it incorrect to say that a functional “maps functions to numbers”?
@user251257: But the dual space of $V$ is also a space consisting of functions :)
Jul
15
comment Sobolev functions counterexample
No, you don't need $C^2$, Lipschitz boundary is sufficient. A function in $H^1$ belongs to $H_0^1$ iff the trace is zero. And a function in $H^2$ belongs to $H_0^2$ iff the traces of the function and its gradient are zero.