List questions from sobolev-spaces

Published on 10 Apr 2026 - 5:27

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Prove a sequence of Weak Solution is Cauchy

Published on 12 Apr 2026 - 2:45

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Continuously differentiable functions is closed in $H^1(\Omega)$

Published on 11 Apr 2026 - 2:16

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If $\phi \in H^{2,p'}$ and $\phi^+ \in H^1_0$, is it true that $\phi \in L^p$? And that $\phi$ in $H^{1,2}$?

Published on 16 Apr 2026 - 13:04

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If the distributional derivatives are locally in $L^2$, can we conclude that the function is locally in $L^2$

Published on 12 Apr 2026 - 17:36

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Reference for discrete interpolation inequalities.

Published on 10 Apr 2026 - 18:14

70

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Brezis Analysis Problem about solutions of $-\Delta u=V(x) e^{u}$

Published on 09 Apr 2026 - 23:40

69

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If a finite Radon measure admits a derivative then it is of the form $u d\mathcal{L}^N$

Published on 14 Apr 2026 - 3:38

85

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Why is the completion $Y$ of a normed space $X$ equipped with the norm $\lVert\cdot\rVert_X$?

Published on 15 Apr 2026 - 6:10

63

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Prove properties about equation $-u’’+u=u^p$

Published on 13 Apr 2026 - 19:09

48

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Density of compactly supported functions on a clopen set

Published on 11 May 2026 - 4:15

59

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The functional $\int_{\Omega} |\nabla u|^p dx$ is invariant under dialation and translation in $\mathbb{R}^N$. How?

Published on 14 Apr 2026 - 4:32

219

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is the absolute value of function $H^s$ also in $H^s$?

Published on 11 Apr 2026 - 9:31

91

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Weighted Poincaré Inequality on unbounded set?

Published on 04 May 2026 - 21:43

99

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Proving $\|\nabla u\|_{L^2(\Omega)}$ is a norm in $H^1_0(\Omega)$, with $\Omega$ a polygonal domain

Published on 14 Apr 2026 - 22:02

List Question

Proof of the Meyers–Serrin theorem (the "$H=W$" theorem)

Prove a sequence of Weak Solution is Cauchy

Continuously differentiable functions is closed in $H^1(\Omega)$

If $\phi \in H^{2,p'}$ and $\phi^+ \in H^1_0$, is it true that $\phi \in L^p$? And that $\phi$ in $H^{1,2}$?

If the distributional derivatives are locally in $L^2$, can we conclude that the function is locally in $L^2$

Reference for discrete interpolation inequalities.

Brezis Analysis Problem about solutions of $-\Delta u=V(x) e^{u}$

If a finite Radon measure admits a derivative then it is of the form $u d\mathcal{L}^N$

Why is the completion $Y$ of a normed space $X$ equipped with the norm $\lVert\cdot\rVert_X$?

Prove properties about equation $-u’’+u=u^p$

Density of compactly supported functions on a clopen set

The functional $\int_{\Omega} |\nabla u|^p dx$ is invariant under dialation and translation in $\mathbb{R}^N$. How?

is the absolute value of function $H^s$ also in $H^s$?

Weighted Poincaré Inequality on unbounded set?

Proving $\|\nabla u\|_{L^2(\Omega)}$ is a norm in $H^1_0(\Omega)$, with $\Omega$ a polygonal domain

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