List questions from sobolev-spaces

Published on 13 Jul 2020 - 19:01

61

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Why does this inequality hold? [Sobolev Embedding]

Published on 16 Jul 2020 - 14:01

77

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Proof Check Sobolev $H^m(\Omega)$ and Riez representation.

Published on 17 Jul 2020 - 8:37

58

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Is there compact Sobolev embedding for functions with target a more general space than $\mathbb{R}^n$?

Published on 18 Jul 2020 - 12:14

113

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Does the distributional antiderivative of a $L^p$ function always exist?

Published on 30 Mar 2026 - 14:57

51

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How to justify that $\Vert u_n - u\Vert_{W_0^{1,p}}\rightarrow 0?$

Published on 20 Jul 2020 - 16:49

691

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Different norms for the $H^{1/2}$ sobolev spaces

Published on 25 Mar 2026 - 6:19

57

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Finding $\varphi$ that verifies the following conditions

Published on 27 Mar 2026 - 1:50

159

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Interpolation theorem on$(0,2 \pi)$. Suppose $f \in L^2$ , the distribution derivative $f'' \in L^2$ ,then can we show that $f' \in L^2$?

Published on 23 Jul 2020 - 16:02

84

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Prove that the functional in $C_c^0(\Omega)$ is a Radon measure

Published on 28 Mar 2026 - 11:28

768

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Product of two functions in $H^1$( or $W^{1,2}$) is in $H^{\frac{1}{2}}$.

Published on 30 Mar 2026 - 14:59

53

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Subspace of $H^1(\Omega)$ is closed?

Published on 25 Jul 2020 - 19:30

705

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Weak Convergence in $W^{1,2}(D)$ implies strong convergence in $L^{2}(D)$

Published on 27 Jul 2020 - 15:39

45

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Necessary condition on smoothness parameter for Strichartz estimates

Published on 02 Mar 2026 - 10:23

139

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Does such a Sobolev space exist in literature?

Published on 27 Jul 2020 - 18:15

List Question

$W^{m,p}_{0}(\mathbb{R}^d) = W^{m,p}(\mathbb{R}^d)$ and continuously imbedded

Why does this inequality hold? [Sobolev Embedding]

Proof Check Sobolev $H^m(\Omega)$ and Riez representation.

Is there compact Sobolev embedding for functions with target a more general space than $\mathbb{R}^n$?

Does the distributional antiderivative of a $L^p$ function always exist?

How to justify that $\Vert u_n - u\Vert_{W_0^{1,p}}\rightarrow 0?$

Different norms for the $H^{1/2}$ sobolev spaces

Finding $\varphi$ that verifies the following conditions

Interpolation theorem on$(0,2 \pi)$. Suppose $f \in L^2$ , the distribution derivative $f'' \in L^2$ ,then can we show that $f' \in L^2$?

Prove that the functional in $C_c^0(\Omega)$ is a Radon measure

Product of two functions in $H^1$( or $W^{1,2}$) is in $H^{\frac{1}{2}}$.

Subspace of $H^1(\Omega)$ is closed?

Weak Convergence in $W^{1,2}(D)$ implies strong convergence in $L^{2}(D)$

Necessary condition on smoothness parameter for Strichartz estimates

Does such a Sobolev space exist in literature?

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