List questions from sobolev-spaces

Published on 25 Mar 2026 - 15:10

40

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If $\Omega\subseteq\mathbb R^d$ is sufficiently nice, does it hold $L^\infty(\Omega)\subseteq H^1(\Omega)$?

Published on 14 Apr 2026 - 4:27

108

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Sufficient conditions for derviative of this product to be in $L^2$.

Published on 16 Apr 2026 - 8:25

230

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Show that $W^{s_2, 2}(\mathbb{T}) \hookrightarrow W^{s_1,2} (\mathbb{T})$ is a compact operator

Published on 15 Apr 2026 - 13:23

47

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Minimum of an energy functional over a closed and convex set

Published on 12 Apr 2026 - 9:30

23

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Can we show that every function in $C_c^k((0,T),V)$ can be approximated by a product $\tau v$, where $\tau\in C^\infty((0,T))$ and $v\in V$?

Published on 15 Apr 2026 - 9:15

176

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Sobolev's inequality for $n<p<\infty$ and $n=p$ with $U$ open bounded set

Published on 15 Apr 2026 - 18:42

43

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Prove if $u_n \in W^{1,p}$ such that $u_n\to u$ in $L^p$ and $u_n'$ is uniformly bounded in $L_p$ then $u \in W^{1,p}$

Published on 15 Apr 2026 - 8:32

460

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Which Sobolev spaces are function spaces?

Published on 09 Apr 2026 - 7:23

159

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Prove $H^1(\Omega) = H^1_0(\Omega)$ for $\Bbb{R}^N\setminus \{0\}$

Published on 17 Apr 2026 - 0:29

287

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About the trace inequality in Sobolev space

Published on 25 Mar 2026 - 14:20

54

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$D^*$ invertible iff $D$ invertible but with unexpected inner products.

Published on 13 Apr 2026 - 19:38

53

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How to show if result hold for $C_{0}^{\infty}(\Omega)$ then also hold for $ W_{0}^{1, p}(\Omega)$?

Published on 14 Apr 2026 - 21:19

89

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Question regarding $W_0^{1,2}$, Propriety of $u_+$

Published on 16 Apr 2026 - 11:18

54

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Variational Problem has no minimizer

Published on 12 Apr 2026 - 7:43

List Question

An estimate for singular integral.

If $\Omega\subseteq\mathbb R^d$ is sufficiently nice, does it hold $L^\infty(\Omega)\subseteq H^1(\Omega)$?

Sufficient conditions for derviative of this product to be in $L^2$.

Show that $W^{s_2, 2}(\mathbb{T}) \hookrightarrow W^{s_1,2} (\mathbb{T})$ is a compact operator

Minimum of an energy functional over a closed and convex set

Can we show that every function in $C_c^k((0,T),V)$ can be approximated by a product $\tau v$, where $\tau\in C^\infty((0,T))$ and $v\in V$?

Sobolev's inequality for $n<p<\infty$ and $n=p$ with $U$ open bounded set

Prove if $u_n \in W^{1,p}$ such that $u_n\to u$ in $L^p$ and $u_n'$ is uniformly bounded in $L_p$ then $u \in W^{1,p}$

Which Sobolev spaces are function spaces?

Prove $H^1(\Omega) = H^1_0(\Omega)$ for $\Bbb{R}^N\setminus \{0\}$

About the trace inequality in Sobolev space

$D^*$ invertible iff $D$ invertible but with unexpected inner products.

How to show if result hold for $C_{0}^{\infty}(\Omega)$ then also hold for $ W_{0}^{1, p}(\Omega)$?

Question regarding $W_0^{1,2}$, Propriety of $u_+$

Variational Problem has no minimizer

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