List questions from sobolev-spaces

Published on 26 Mar 2026 - 4:14

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the basis for the Sobolev space $H^1_0([0,1],\mathbb{R})$

Published on 16 Apr 2026 - 13:08

410

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PDE with measure-valued right hand sides?

Published on 14 Apr 2026 - 13:23

86

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about the functions of $L^2(0,T;H^{1}_{0} (U))$

Published on 16 Apr 2026 - 10:40

606

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about the proof of existence of weak solution of linear hyperbolic equation ( via Galerkin method)

Published on 11 Apr 2026 - 2:44

72

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Is there a function $u$ with $g(u)$ regular whose "truncation" $g(T(u))$ is not regular?

Published on 12 Apr 2026 - 7:03

1.3k

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Is integration by parts valid here for this Sobolev function?

Published on 12 Apr 2026 - 21:25

332

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variational problem-exercice

Published on 10 Apr 2026 - 23:42

95

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$H^1$ estimate by $L^2$-norm

Published on 16 Apr 2026 - 6:29

163

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Variational problem - continuity exercise

Published on 10 Apr 2026 - 17:25

4.1k

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Why do we need semi-norms on Sobolev-spaces?

Published on 13 Apr 2026 - 0:04

212

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Holomorphic Extension of a Sobolev Function is Sobolev

Published on 13 Apr 2026 - 13:46

90

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Need a source for the following result: From $v \in H^1$ and $f$ Lipschitz it follows that $f(v) \in H^1$.

Published on 14 Apr 2026 - 23:59

1.4k

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$u\in W_0^{1,p}(\Omega)$ but it's extension by zero does not belong to $W^{1,p}_0(\mathbb{R}^N)$

Published on 16 Apr 2026 - 9:06

1.1k

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Is tensor product of Sobolev spaces dense?

Published on 10 Apr 2026 - 20:23

List Question

$f\in L^2(\mathbb{R}^3)$ implies $v(x)=\int_{\mathbb{R}^3}\frac{f(y)}{|x-y|}dy\in W^{2,2}$?

the basis for the Sobolev space $H^1_0([0,1],\mathbb{R})$

PDE with measure-valued right hand sides?

about the functions of $L^2(0,T;H^{1}_{0} (U))$

about the proof of existence of weak solution of linear hyperbolic equation ( via Galerkin method)

Is there a function $u$ with $g(u)$ regular whose "truncation" $g(T(u))$ is not regular?

Is integration by parts valid here for this Sobolev function?

variational problem-exercice

$H^1$ estimate by $L^2$-norm

Variational problem - continuity exercise

Why do we need semi-norms on Sobolev-spaces?

Holomorphic Extension of a Sobolev Function is Sobolev

Need a source for the following result: From $v \in H^1$ and $f$ Lipschitz it follows that $f(v) \in H^1$.

$u\in W_0^{1,p}(\Omega)$ but it's extension by zero does not belong to $W^{1,p}_0(\mathbb{R}^N)$

Is tensor product of Sobolev spaces dense?

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