List questions from sobolev-spaces

Published on 05 May 2026 - 9:37

53

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Examples showing that Sobolev embedding is optimal for a bounded domain?

Published on 12 Apr 2026 - 11:47

45

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Existence of $\phi\in C_{0}^{\infty}(\Omega)$

Published on 12 Apr 2026 - 19:17

52

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Inclusion of Sobolev spaces $H^2(\mathbb{R^2}) \subset W^{1,4}(\mathbb{R^2})$?

Published on 14 Apr 2026 - 13:33

121

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Embedding of $W^{1,n}(U)\hookrightarrow L^q(U)$

Published on 16 Apr 2026 - 2:14

288

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Energy norm/ Proof of the axiom of the norm

Published on 11 Apr 2026 - 0:02

357

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Weak formulation of $\Delta^{2}u=f$ with boundary conditions $u=\Delta u =0$.

Published on 13 Apr 2026 - 20:15

21

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Can we deduce $f^p\in W^{1,1}(U)$ if $f\in W^{1,p}(U)$

Published on 17 Apr 2026 - 1:11

46

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compute the following weak derivative $D(|u|^{p/2-1} u)=p/2|u|^{p/2-1} Du$ in Sobolev space

Published on 17 Apr 2026 - 6:10

26

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In which space is this sequence converging?

Published on 14 Apr 2026 - 11:54

66

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Fermat Theorem for weak derivatives?

Published on 13 Apr 2026 - 11:47

289

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The Heaviside Function, its Fourier transform, and its inclusion in $H^s(\mathbb{R})$ for all $s<1/2$.

Published on 11 Apr 2026 - 13:42

32

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How can I find Sobolev generalized derivative of function $f(t)$

Published on 15 Apr 2026 - 14:02

443

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Density in negative Sobolev spaces

Published on 11 Apr 2026 - 0:58

41

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The integral $\int_{U}u^{4}$ is well-defined for $u\in H_{0}^{2}(U)$ and $U\subset\mathbb{R}^{n}$ open, bounded, $n\leq3$.

Published on 15 Apr 2026 - 11:40

List Question

Counter example in Sobolev space

Examples showing that Sobolev embedding is optimal for a bounded domain?

Existence of $\phi\in C_{0}^{\infty}(\Omega)$

Inclusion of Sobolev spaces $H^2(\mathbb{R^2}) \subset W^{1,4}(\mathbb{R^2})$?

Embedding of $W^{1,n}(U)\hookrightarrow L^q(U)$

Energy norm/ Proof of the axiom of the norm

Weak formulation of $\Delta^{2}u=f$ with boundary conditions $u=\Delta u =0$.

Can we deduce $f^p\in W^{1,1}(U)$ if $f\in W^{1,p}(U)$

compute the following weak derivative $D(|u|^{p/2-1} u)=p/2|u|^{p/2-1} Du$ in Sobolev space

In which space is this sequence converging?

Fermat Theorem for weak derivatives?

The Heaviside Function, its Fourier transform, and its inclusion in $H^s(\mathbb{R})$ for all $s<1/2$.

How can I find Sobolev generalized derivative of function $f(t)$

Density in negative Sobolev spaces

The integral $\int_{U}u^{4}$ is well-defined for $u\in H_{0}^{2}(U)$ and $U\subset\mathbb{R}^{n}$ open, bounded, $n\leq3$.

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