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Answer by Changyu Guo for Sobolev spaces on boundaries
One more remark on the definition of Sobolev spaces. Given a general metric measure space $(X,d,\mu)$, where $(X,d)$ is a metric space and $\mu$ is a locally finite Borel measure on $X$, one has at...
View ArticleAnswer by timur for Sobolev spaces on boundaries
1) Yes it is that simple. It is a special case of the so called Slobodeckij norm for Sobolev and more generally Besov spaces.2) Not as much a need as it offers you a different perspective. Note that...
View ArticleSobolev spaces on boundaries
Consider the Sobolev space $W^{s,2}=H^s$ for $s=\frac{1}{2}.$Let $\Omega \subset \mathbb{R}^n$ be an open set with boundary $\partial\Omega$. I have seen two definitions of the space...
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