Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with sobolev-spaces
Search options not deleted
user 50777
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.
4
votes
Accepted
Is the product of $u \in W^{\sigma,1}(\Omega)$ and $v \in C^{0,\sigma}(\Omega)$ again in $W^...
It is not true that $W^{\sigma,1} \times C^{0,\sigma} \hookrightarrow W^{\sigma,1}$ with $\Omega = \mathbb{R}^n$.
My reference for such questions is
Thomas Runst, and Winfried Sickel. Sobolev spaces …
- 981
7
votes
Can we interpret fractional Sobolev spaces in terms of fractional derivatives?
Yes, such an interpretation exists, at least in the following case.
Take $p = 2$, $n = 1$ and $\Omega = (0,1)$. Then, for $0 < s < 1$,
$$
\| f \|_{H^s(0,1)} \approx \| \partial_t^s f \|_{L^2(0,1)}
$$ …
- 981
3
votes
Sobolev inequality with holes
It looks like you are looking for the extreme case of a Gagliardo-Nirenberg interpolation inequality, in the case of an exterior domain (that is, an unbounded domain with compact boundary). Such inequ …
- 981
3
votes
The compact embedding of $H^{1/2}_{2\pi}$ in $L^s(0, 2\pi)$
I would say that the book Linear and Quasilinear Parabolic Problems, Volume II: Function Spaces by Herbert Amann qualifies as a modern reference (published in 2019).
You can find a version of a Rellic …
- 981
5
votes
1
answer
629
views
Hardy-Littlewood-Sobolev inequality using fractional sobolev norm on the RHS
Using Hardy-Littlewood-Sobolev inequality, we can prove that:
$$\left| \int_0^1\int_0^1 |x-y|^{-\frac{1}{2}} f(x)f(y) \mathrm{d}x \mathrm{d}y \right| \leq C \left\| f \right\|_{L^{4/3}(0,1)}^2 \leq C …
- 981
2
votes
Bound for the product of Sobolev functions in $W^{s,1}$
I believe that $W^{s,1}(\mathbb{R}^d)$ is a Banach algebra when $s > d$.
This is a particular case of Theorem 7.3 of the paper Multiplication in Sobolev spaces by Ali Behzadan and Michael Holst.
- 981