List questions from sobolev-spaces

Published on 10 Apr 2026 - 19:30

420

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What do we need Sobolev-spaces $W^{k, p}$ with $p \neq 2$ for?

Published on 16 Apr 2026 - 9:14

37

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Is true that $\sum_{|\alpha|=k}\sum_{|\beta|=m-k}\|D^{\alpha+\beta}u\|^p_{L_{p}(\Omega)}=|u|_{W^{m,p}(\Omega)}^p$?

Published on 28 Mar 2026 - 10:24

689

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The Laplacian is an isomorphism between $W^{1,p}_0(\Omega)$ and $W^{-1,p}(\Omega)$

Published on 16 Apr 2026 - 10:49

275

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Take $U= B^{0}(0,1)$ to be the unit ball in $\mathbb R^n$ and consider $u(x)=|x|^{-\alpha}$ ($x \in U$, $x \neq 0$).

Published on 16 Apr 2026 - 2:35

169

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Derivatives in Sobolev spaces involving time

Published on 11 Apr 2026 - 12:28

70

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If $V$ is closed in $H^m(\Omega),\,m\geq1,$ is it also closed in $L^2(\Omega)$?

Published on 12 Apr 2026 - 9:53

104

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Exercise about a functional and sobolev spaces

Published on 11 Apr 2026 - 9:25

257

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Exercise on equivalence of weak convergence in Sobolev and $L^p$ spaces

Published on 17 Apr 2026 - 12:20

44

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Looking for citation for basic result about generalized functions (described in question)

Published on 13 Apr 2026 - 14:08

26

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Extension zero of $W^{k,p}(\Omega)$ function

Published on 11 Apr 2026 - 14:44

653

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Space of locally Sobolev functions

Published on 15 Apr 2026 - 17:55

36

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function is a fourier transform for integrable function

Published on 13 Apr 2026 - 21:13

597

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Existence of time derivative in Bochner space $L^2(0,T;H_0^1(U))$ (parabolic pde)

Published on 26 Mar 2026 - 16:07

567

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Product rule and integration by parts in Bochner Sobolev space $W^{1,1}(U)$

Published on 11 Apr 2026 - 23:59

List Question

trace embedding in fractional sobolev space

What do we need Sobolev-spaces $W^{k, p}$ with $p \neq 2$ for?

Is true that $\sum_{|\alpha|=k}\sum_{|\beta|=m-k}\|D^{\alpha+\beta}u\|^p_{L_{p}(\Omega)}=|u|_{W^{m,p}(\Omega)}^p$?

The Laplacian is an isomorphism between $W^{1,p}_0(\Omega)$ and $W^{-1,p}(\Omega)$

Take $U= B^{0}(0,1)$ to be the unit ball in $\mathbb R^n$ and consider $u(x)=|x|^{-\alpha}$ ($x \in U$, $x \neq 0$).

Derivatives in Sobolev spaces involving time

If $V$ is closed in $H^m(\Omega),\,m\geq1,$ is it also closed in $L^2(\Omega)$?

Exercise about a functional and sobolev spaces

Exercise on equivalence of weak convergence in Sobolev and $L^p$ spaces

Looking for citation for basic result about generalized functions (described in question)

Extension zero of $W^{k,p}(\Omega)$ function

Space of locally Sobolev functions

function is a fourier transform for integrable function

Existence of time derivative in Bochner space $L^2(0,T;H_0^1(U))$ (parabolic pde)

Product rule and integration by parts in Bochner Sobolev space $W^{1,1}(U)$

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