# Tagged Questions

For questions about or related to Sobolev spaces, which are function spaces equipped with a norm combining norms of a function and its derivatives.

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### Splitting the region and estimating fractional Sobolev norms

I've been reading the paper "On the Bourgain, Brezis, and Mironescu Theorem Concerning Limiting Embeddings of Fractional Sobolev Spaces" by Maz'ya and Shaposhnikova and struggling with the short style ...
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### seeking for a general strategy to identify the right space for the domain of semigroup generator

I wish to show the domain of a strongly continuous semigroup $S(t)$ is some sobolev space, for instance, for the heat semigroup, it is known that $$D(A)=W^{2,p}$$ I believe a general strategy to get ...
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### antiderivative of $\psi'(u)$ for $u\in W^{1,2}_0((a,b))$

Let $u\in W^{1,2}_0((a,b))$ and $\psi'$ the derivative of a convex function $\Psi\in C^1(\mathbb{R})$. If I want to consider the antiderivative of $\psi'(u)$, what happens with the $u$ inside $\Psi(u)$...
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### Mollification of functions in $L^2(0,T;H^1)\cap H^1(0,T;H^{-1})$

Let $u \in L^2(0,T;H^1(\Omega))\cap H^1(0,T;H^{-1}(\Omega))$ where $\Omega \subset \mathbb{R}^n$ is a bounded domain. I know that (eg. from Wloka or Hunter's PDE notes) that there is a mollification ...