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seen Apr 13 at 16:20

Dec
22
asked Finest topology on a space of banach space operators
Dec
17
comment Dual of Sobolev space $W^{1,p}(U)$ for $U$ an arbitrary subset of $\mathbb R^n$
Let $X$ be the (closed) image of the embedding into $Z = L^p \times (L^p)^n$ as described by you. Let $Y$ be the subspace of $Z'$ that vanishes on $X$. Then $X' \equiv Z'/Y$. We have $Z' = L^q \times (L^q)^n$. How do you employ the Hahn-Banach theorem?
Dec
17
asked Intuition for not-so-smooth manifolds
Dec
16
comment Dual of Sobolev space $W^{1,p}(U)$ for $U$ an arbitrary subset of $\mathbb R^n$
You are right. $W^{1,p'} \subset (W^{1,p})'$, whilst for cases of sufficient regularity, as in case $p > n$ by Morrey's lemma, the dirac delta is already a continuous dual vector. However, I find it hard to give the space $(W^{1,p}(\mathbb R^n))'$ a 'nice' characterization.
Dec
15
revised Dual of Sobolev space $W^{1,p}(U)$ for $U$ an arbitrary subset of $\mathbb R^n$
edited title
Dec
15
asked Dual of Sobolev space $W^{1,p}(U)$ for $U$ an arbitrary subset of $\mathbb R^n$
Dec
10
comment Using 4 '8's, get the number 24
This uses only four eights: 8 + 8 + 8 + 8 - 7 - 1 ;-)
Dec
9
awarded  Commentator
Dec
9
comment Distribution whose singular support is open
Thanks, that is a good point to proceed.
Dec
9
asked Distribution whose singular support is open
Dec
4
accepted A smooth function's domain of being non-analytic
Dec
4
asked A smooth function's domain of being non-analytic
Dec
3
accepted Distinction between 'adjoint' and 'formal adjoint'
Dec
3
comment Relation between the norms on X and Y and the induced product norm on X x Y
In fact, you can 'combine' the two norms and $X$ and $Y$ using any norm on $\mathbb R^2$, for example lp-norms. For $p=1$, you obtain you original product norm.
Dec
3
comment Distinction between 'adjoint' and 'formal adjoint'
No. My lecturer has not been able to explain it, too.
Dec
3
asked Distinction between 'adjoint' and 'formal adjoint'
Dec
1
accepted Switching Limits and Suprema
Dec
1
asked Switching Limits and Suprema
Nov
21
accepted When to exchange integration and application of a distribution
Nov
21
accepted p-seminorms on smooth functions are equivalent