List questions from sobolev-spaces

Published on 10 Apr 2026 - 23:58

39

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Question about error analysis, and why the choice of the norm is important

Published on 09 Apr 2026 - 4:42

108

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Fourier coefficients implies absolutely continuity

Published on 11 Apr 2026 - 16:23

35

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Weak convergence and tensors

Published on 17 Apr 2026 - 20:34

159

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How do I find condition on $f$?

Published on 12 Apr 2026 - 14:49

89

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Sobolev injections in $\mathbb{R}$

Published on 12 Apr 2026 - 8:05

138

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If $f$ is continuous and $u \in C^0 \cap H^k$, then is it true that $f(u) \in H^{k}$?

Published on 13 Apr 2026 - 21:17

105

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Proving a Sobolev norm inequality

Published on 14 Apr 2026 - 12:15

76

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A homework question on compact embedding of Sobolev spaces

Published on 14 Apr 2026 - 2:09

63

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Orthogonal representation - Weyl decomposition

Published on 12 Apr 2026 - 22:03

52

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what $H^1_q$ is?

Published on 14 Apr 2026 - 14:49

76

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Extend inequality from dense subset to $H^{1}$

Published on 13 Apr 2026 - 21:24

84

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A subspace of the $H_{0}^1(\Omega) \cap H^2(\Omega)$ is dense in a subspace of $L^2(\Omega)$?

Published on 15 Apr 2026 - 18:48

271

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If $u\in H^s(\mathbb R^d),\,s>d/2$, then $\|u\|_{L^\infty(\mathbb R^d)}\leq C\|u\|_{H^s(\mathbb R^d)}$ via Fourier transform

Published on 14 Apr 2026 - 8:48

45

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$\|u\| _{L^r(\mathbb R^d)}\leq C\|u\| _{L^q(\mathbb R^d)}^{1-\theta}\|Du\| _{L^p(\mathbb R^d)}^{\theta}\forall u\in\mathcal C^{\infty}_c(\mathbb R^d)$

Published on 16 Apr 2026 - 1:23

List Question

Prove that inner space is incomplete and operator is bounded

Question about error analysis, and why the choice of the norm is important

Fourier coefficients implies absolutely continuity

Weak convergence and tensors

How do I find condition on $f$?

Sobolev injections in $\mathbb{R}$

If $f$ is continuous and $u \in C^0 \cap H^k$, then is it true that $f(u) \in H^{k}$?

Proving a Sobolev norm inequality

A homework question on compact embedding of Sobolev spaces

Orthogonal representation - Weyl decomposition

what $H^1_q$ is?

Extend inequality from dense subset to $H^{1}$

A subspace of the $H_{0}^1(\Omega) \cap H^2(\Omega)$ is dense in a subspace of $L^2(\Omega)$?

If $u\in H^s(\mathbb R^d),\,s>d/2$, then $\|u\|_{L^\infty(\mathbb R^d)}\leq C\|u\|_{H^s(\mathbb R^d)}$ via Fourier transform

$\|u\| _{L^r(\mathbb R^d)}\leq C\|u\| _{L^q(\mathbb R^d)}^{1-\theta}\|Du\| _{L^p(\mathbb R^d)}^{\theta}\forall u\in\mathcal C^{\infty}_c(\mathbb R^d)$

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