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Results tagged with sobolev-spaces
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user 33350
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
-1
votes
1
answer
142
views
A suitable Sobolev-type space
Let $\Omega$ be a domain in $\mathbb{R}^3$, does there exist a vector-valued Sobolev-type space, or maybe space in other sense, $V$, satisfying the following:
1) $S:=\lbrace v\in V:\|v\|_{L^\infty(\Om …
- 63
6
votes
1
answer
1k
views
Compactness in Sobolev spaces
I was wondering whether the set $\lbrace f\in H_0^1(\Omega)|\|f\|_{L^\infty(\Omega)}\leq 1\rbrace$ is compact in $H_0^1(\Omega)$ or not. Here $\Omega$ is a convex domain in $\mathbb{R}^3$ with Lipschi …
- 63
0
votes
1
answer
312
views
Is BV2 space closed in L2 space?
We define the BV2 space by
$S = \lbrace f\in L^2:\textrm{TV}(f)<\infty\rbrace$, where $TV(f)=\sup_{g\in C_c^1,\|g\|_\infty\leq 1}\int f\cdot \textrm{div}g$.
My question is: is $S$ closed in $L^2$?
T …
- 63