List questions from fractional-sobolev-spaces

Published on 28 Jul 2021 - 18:00

49

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compactness of a sequence in $W^{-1,q}$

Published on 11 Aug 2021 - 18:46

120

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Why is $W^{s,p}(\mathbb R^n)$ continuously embedded in $L^q(\mathbb R^n)$ for $q\in[p,\frac{np}{n-sp}]$, given the fractional Sobolev inequality?

Published on 12 Aug 2021 - 3:59

437

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Trace theorem for general Sobolev spaces

Published on 14 Aug 2021 - 20:47

48

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Prove that $\int_U u^2\le C\int_U\int_U\frac{(u(x)-u(y))^2}{|x-y|^{n+2s}}dx\,dy$ for some $C>0$

Published on 17 Aug 2021 - 16:19

82

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Does this function live in $H^{\frac{1}{2}}(\partial \Omega)$

Published on 06 Sep 2021 - 7:31

74

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closeness of Sobolev space under multiplication by a periodic function

Published on 19 Sep 2021 - 4:51

80

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Example of a distribution in $H^{-\varepsilon}(\mathbb R^n)$ with small $\varepsilon>0$ that is not a locally integrable function

Published on 27 Sep 2021 - 9:21

77

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$\delta \in H^{-s}(\mathbb{R}^n)$ for $s>\frac{n}{2}$

Published on 07 Oct 2021 - 20:26

181

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Estimate of supremum of a function by an integral

Published on 10 Oct 2021 - 19:39

71

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Showing that every weak solution in a pseudo differential equation with elliptic symbol is in Sobolev space.

Published on 22 Oct 2021 - 6:56

47

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If $u$ is a function between two functions in $H_{0}^{s}(\Omega).$ Then $u$ is in $H_{0}^{s}(\Omega)$ too?

Published on 26 Oct 2021 - 14:31

56

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Proving $(1+|\xi|^2)^{-s/2}\widehat{u} \in L^2(\mathbb{R}^n)$

Published on 31 Oct 2021 - 6:48

39

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$H^{-3/2}$ control of the laplacian of a function by means of $H^{1/2}$ norm in $\mathbb{R}^2$

Published on 06 Dec 2021 - 21:47

291

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Restriction of fractional Sobolev "function" of negative order to subset

Published on 25 Mar 2026 - 15:42

List Question

Global integral estimate in $\mathbb{R}^N$

compactness of a sequence in $W^{-1,q}$

Why is $W^{s,p}(\mathbb R^n)$ continuously embedded in $L^q(\mathbb R^n)$ for $q\in[p,\frac{np}{n-sp}]$, given the fractional Sobolev inequality?

Trace theorem for general Sobolev spaces

Prove that $\int_U u^2\le C\int_U\int_U\frac{(u(x)-u(y))^2}{|x-y|^{n+2s}}dx\,dy$ for some $C>0$

Does this function live in $H^{\frac{1}{2}}(\partial \Omega)$

closeness of Sobolev space under multiplication by a periodic function

Example of a distribution in $H^{-\varepsilon}(\mathbb R^n)$ with small $\varepsilon>0$ that is not a locally integrable function

$\delta \in H^{-s}(\mathbb{R}^n)$ for $s>\frac{n}{2}$

Estimate of supremum of a function by an integral

Showing that every weak solution in a pseudo differential equation with elliptic symbol is in Sobolev space.

If $u$ is a function between two functions in $H_{0}^{s}(\Omega).$ Then $u$ is in $H_{0}^{s}(\Omega)$ too?

Proving $(1+|\xi|^2)^{-s/2}\widehat{u} \in L^2(\mathbb{R}^n)$

$H^{-3/2}$ control of the laplacian of a function by means of $H^{1/2}$ norm in $\mathbb{R}^2$

Restriction of fractional Sobolev "function" of negative order to subset

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