List questions from sobolev-spaces

Published on 21 Oct 2016 - 10:37

28

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Show that $|x|\in H^1(-1,1)$.

Published on 22 Oct 2016 - 12:58

159

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$\int_0^T\int_Ω\langle(u_n\cdot\nabla)w,u_n\rangle dxdt\to\int_0^T\int_Ω\langle(u\cdot\nabla)w,u\rangle dxdt$ if $u_n\to u$ weakly and strongly

Published on 23 Oct 2016 - 19:46

1.6k

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Proving $|x|^{-\alpha} \in W^{1,p}(U)$

Published on 26 Mar 2026 - 14:19

93

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On a subspace of a Sobolev space

Published on 24 Oct 2016 - 7:26

68

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Search for a reference on characterising Lebesgue spaces in terms of (inhomogeneous) Besov spaces.

Published on 28 Mar 2026 - 9:36

83

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Example of functions in $W^{1,n}(\mathbb{R}^n)$ but not in $L^1(\mathbb{R}^n)$?

Published on 25 Oct 2016 - 1:08

222

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Help proving an inequlity using Young's inequality for discrete convolutions and Cauchy-Schwarz

Published on 26 Oct 2016 - 13:24

133

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The limit of total variation minimizer goes to the average

Published on 26 Mar 2026 - 17:35

87

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Smoothing inside the null-space of a partial differential operator

Published on 25 Mar 2026 - 3:07

445

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Density of smooth compactly supported functions in Sobolev space in bounded domain

Published on 31 Mar 2026 - 8:31

26

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convergence of norm with respect to the order of sobolev norm?

Published on 31 Oct 2016 - 18:26

511

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The Minkowski inequality for fractional order?

Published on 31 Oct 2016 - 20:32

503

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minimize a sum of weighted square distances

Published on 23 Feb 2026 - 4:39

1.4k

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Gradient of Sobolev function on level sets

Published on 26 Mar 2026 - 17:29

List Question

Extension by zero of functions of H^1

Show that $|x|\in H^1(-1,1)$.

$\int_0^T\int_Ω\langle(u_n\cdot\nabla)w,u_n\rangle dxdt\to\int_0^T\int_Ω\langle(u\cdot\nabla)w,u\rangle dxdt$ if $u_n\to u$ weakly and strongly

Proving $|x|^{-\alpha} \in W^{1,p}(U)$

On a subspace of a Sobolev space

Search for a reference on characterising Lebesgue spaces in terms of (inhomogeneous) Besov spaces.

Example of functions in $W^{1,n}(\mathbb{R}^n)$ but not in $L^1(\mathbb{R}^n)$?

Help proving an inequlity using Young's inequality for discrete convolutions and Cauchy-Schwarz

The limit of total variation minimizer goes to the average

Smoothing inside the null-space of a partial differential operator

Density of smooth compactly supported functions in Sobolev space in bounded domain

convergence of norm with respect to the order of sobolev norm?

The Minkowski inequality for fractional order?

minimize a sum of weighted square distances

Gradient of Sobolev function on level sets

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