List questions from sobolev-spaces

Published on 13 Apr 2026 - 1:07

105

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The embedding $W^{2,2} (\Omega)\hookrightarrow L^\infty(\Omega)$

Published on 13 Apr 2026 - 0:18

145

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High-order Sobolev function on sphere

Published on 12 Apr 2026 - 13:01

68

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Are the translates of a function in $H^1(\mathbb{R}^2)$ bounded by a function with finite integral over some compact set?

Published on 07 Apr 2026 - 23:04

63

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Proof of an identity in a Lebesgue-Bochner space

Published on 26 Mar 2026 - 19:19

49

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Laplacian in $L^2$

Published on 16 Apr 2026 - 15:17

184

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PDE: A priori estimate

Published on 12 Apr 2026 - 22:11

413

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$L^{2}(\mathbb{R^n})$ is compactly embedded in which space?

Published on 14 Apr 2026 - 20:27

40

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The embedding $W^{1,\infty}(\Omega) \hookrightarrow L^{2}(\Omega)$ for a regular bounded open set $\Omega \subset \mathbb{R}^N$

Published on 16 Apr 2026 - 5:33

182

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Does null Dirichlet condition implies null Neumann condition?

Published on 12 Apr 2026 - 8:21

119

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Reference request: Lebesgue/Sobolev spaces on the boundary

Published on 10 May 2026 - 16:24

70

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Two properties about the sequence $u_n:= v_n +\alpha t_n$, with $v_n$ and $t_n$ bounded

Published on 16 Apr 2026 - 13:15

137

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Why do we need Poincaré inequality to deduce the equivalence of the norms $\|\cdot\|_{H^1_0}$ and $\|\cdot\|_{H^1}$ on $H^1_0(\Omega)$?

Published on 15 Apr 2026 - 0:04

85

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It is true that $\int_{\Omega} |u|^s |\nabla u|^p dx =+\infty$ for some $u\in W_0^{1, p}(\Omega)$?

Published on 14 Apr 2026 - 5:35

50

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techniques to know whether given function is in $H^s(\Omega)$ or not?

Published on 13 Apr 2026 - 4:57

List Question

Minimizer on Sobolev space $H^1 (\Omega)$.

The embedding $W^{2,2} (\Omega)\hookrightarrow L^\infty(\Omega)$

High-order Sobolev function on sphere

Are the translates of a function in $H^1(\mathbb{R}^2)$ bounded by a function with finite integral over some compact set?

Proof of an identity in a Lebesgue-Bochner space

Laplacian in $L^2$

PDE: A priori estimate

$L^{2}(\mathbb{R^n})$ is compactly embedded in which space?

The embedding $W^{1,\infty}(\Omega) \hookrightarrow L^{2}(\Omega)$ for a regular bounded open set $\Omega \subset \mathbb{R}^N$

Does null Dirichlet condition implies null Neumann condition?

Reference request: Lebesgue/Sobolev spaces on the boundary

Two properties about the sequence $u_n:= v_n +\alpha t_n$, with $v_n$ and $t_n$ bounded

Why do we need Poincaré inequality to deduce the equivalence of the norms $\|\cdot\|_{H^1_0}$ and $\|\cdot\|_{H^1}$ on $H^1_0(\Omega)$?

It is true that $\int_{\Omega} |u|^s |\nabla u|^p dx =+\infty$ for some $u\in W_0^{1, p}(\Omega)$?

techniques to know whether given function is in $H^s(\Omega)$ or not?

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