List questions from sobolev-spaces

Published on 02 Apr 2026 - 14:37

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There is no continuous functional $T:L^p(\Omega)\rightarrow L^p(\partial \Omega)$, with $\Omega\subset\mathbb{R}^n$? (As in trace theorem)

Published on 25 Mar 2026 - 7:54

29

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Is there a way to prove the theorem of Trace as in Evans, in the picture below, using only weak derivatives?

Published on 25 Mar 2026 - 7:54

16

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Sobolev embedding for p=N, counterexample

Published on 13 Dec 2023 - 20:40

31

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Convergence of the derivatives implies convergence of the original functions on $1$-dimension.

Published on 23 Feb 2026 - 19:24

20

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Uniform boundedness of sequence of Sobolev extensions

Published on 07 Apr 2026 - 2:06

63

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If $u(.,t) \in H^2(\mathbb{R})$, then $u (.,t) \in C^1(\mathbb{R})$?

Published on 28 Mar 2026 - 8:49

52

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A question approximation with compact support function in $H^s$

Published on 15 Dec 2023 - 7:52

35

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A question on equivalent norms on Sobolev spaces

Published on 15 Dec 2023 - 19:23

72

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Does Weak convergence in $W^{1,p}(\Omega)$ implies almost everywhere of the gradient $\nabla$

Published on 23 Feb 2026 - 17:28

195

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Woud you please check some steps in proof I tried of Trace Theorem from Evans book?

Published on 28 Mar 2026 - 6:00

66

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Prove that the given space $H^1$ is not complete.

Published on 17 Dec 2023 - 14:47

25

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$H^1(\mathbb{R})$ function has a finite moment?

Published on 28 Mar 2026 - 18:14

75

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Terminology for "pointwise convergence on compact subsets"? (Sobolev spaces)

Published on 19 Dec 2023 - 16:00

60

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A problem related to Sobolev space

Published on 20 Dec 2023 - 4:37

List Question

Is correct the following definition of $R^n$ valued Sobolev spaces?

There is no continuous functional $T:L^p(\Omega)\rightarrow L^p(\partial \Omega)$, with $\Omega\subset\mathbb{R}^n$? (As in trace theorem)

Is there a way to prove the theorem of Trace as in Evans, in the picture below, using only weak derivatives?

Sobolev embedding for p=N, counterexample

Convergence of the derivatives implies convergence of the original functions on $1$-dimension.

Uniform boundedness of sequence of Sobolev extensions

If $u(.,t) \in H^2(\mathbb{R})$, then $u (.,t) \in C^1(\mathbb{R})$?

A question approximation with compact support function in $H^s$

A question on equivalent norms on Sobolev spaces

Does Weak convergence in $W^{1,p}(\Omega)$ implies almost everywhere of the gradient $\nabla$

Woud you please check some steps in proof I tried of Trace Theorem from Evans book?

Prove that the given space $H^1$ is not complete.

$H^1(\mathbb{R})$ function has a finite moment?

Terminology for "pointwise convergence on compact subsets"? (Sobolev spaces)

A problem related to Sobolev space

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