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Results tagged with sobolev-spaces
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user 824
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.
11
votes
3
answers
3k
views
History of Sobolev space notations
I would like to know the historical reason why the letter H is used for Sobolev spaces. In particular, why not S? It would be interesting to know the same for the letter W.
- 1
9
votes
3
answers
2k
views
Trace theorem for $C^{k,1}$ domains
What are the best results on (Sobolev space) trace theorems for $C^{k,1}$ domains?
For $k=0$, e.g., when the domain is Lipschitz, from e.g. the works of Martin Costabel and Zhonghai Ding, it is known …
- 446
4
votes
4
answers
4k
views
Variation on the Sobolev space $H^1_0$
Let $\Omega\subset\mathbb{R}^n$ be a bounded open set, let
$$
C^1_0(\overline\Omega) = \{u\in C^1(\Omega)\cap C(\overline\Omega):u|_{\partial\Omega}=0\},
$$
and let $C^1_c(\Omega)$ be the space of co …
- 2,834
5
votes
0
answers
534
views
Moduli of smoothness, Besov spaces, and Sobolev spaces
For $1\leq p\leq\infty$, the $r$-th order $L^p$-modulus of smoothness is
\begin{equation}
\omega_r(u,t,\Omega)_p=\sup_{|h|\leq t}\|\Delta_h^ru\|_{L^p(\Omega_{rh})}
\end{equation}
where $\Omega_{rh}=\{ …
- 3,322