List questions from sobolev-spaces

Published on 12 Apr 2026 - 17:38

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Why $L^2(\Omega) \hookrightarrow H^{-1}$?

Published on 15 Apr 2026 - 5:05

73

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Prove that $ |f(x)| \leq ||f'||_{L^2} \sqrt{x (1 -x)} $ for any $f$ in $W_0^{1,2} ([0, 1])$

Published on 17 Apr 2026 - 16:01

440

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Weak derivative of positive part of Sobolev function

Published on 14 Apr 2026 - 5:31

89

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Why is $D(\Omega)$ continuously embeded in $H_0^1(\Omega)$?

Published on 13 Apr 2026 - 19:37

192

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Proving $D(\Omega)$ is not dense in $H^1(\Omega)$

Published on 12 Apr 2026 - 2:49

273

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Weak solution, Laplace equation.

Published on 11 Apr 2026 - 16:05

125

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Support of a convolution when extending $u\in W^{1,p}_0$ by zero (Brezis Ch 9)

Published on 15 Apr 2026 - 3:18

66

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A property of Sobolev spaces on bounded domains

Published on 15 Apr 2026 - 12:04

48

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Prove that $n \cdot \frac{\partial u}{\partial n} = 0$ for divergence-free functions that vanishes on boundary

Published on 14 Apr 2026 - 21:54

28

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A Laplacian inequality over a closed domain in R^3

Published on 12 Apr 2026 - 3:05

95

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Regularity for a semilinear problem

Published on 11 Apr 2026 - 12:49

70

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A local version of the Sobolev inequality

Published on 15 Apr 2026 - 13:12

63

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If $\boldsymbol{v} \in [W^{1, 2}_{loc}(\overline{\Omega})]^3$, then $\boldsymbol{v}\cdot \nabla v \in [L^{3/2}_{loc}(\overline{\Omega})]^3$.

Published on 15 Apr 2026 - 21:54

177

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Is $(1-x)^{\alpha} \log(1-x)$ a Sobolev function?

Published on 16 Apr 2026 - 1:26

List Question

Problem about multiplication of functions in Sobolev spaces and regularity related to gauge theory

Why $L^2(\Omega) \hookrightarrow H^{-1}$?

Prove that $ |f(x)| \leq ||f'||_{L^2} \sqrt{x (1 -x)} $ for any $f$ in $W_0^{1,2} ([0, 1])$

Weak derivative of positive part of Sobolev function

Why is $D(\Omega)$ continuously embeded in $H_0^1(\Omega)$?

Proving $D(\Omega)$ is not dense in $H^1(\Omega)$

Weak solution, Laplace equation.

Support of a convolution when extending $u\in W^{1,p}_0$ by zero (Brezis Ch 9)

A property of Sobolev spaces on bounded domains

Prove that $n \cdot \frac{\partial u}{\partial n} = 0$ for divergence-free functions that vanishes on boundary

A Laplacian inequality over a closed domain in R^3

Regularity for a semilinear problem

A local version of the Sobolev inequality

If $\boldsymbol{v} \in [W^{1, 2}_{loc}(\overline{\Omega})]^3$, then $\boldsymbol{v}\cdot \nabla v \in [L^{3/2}_{loc}(\overline{\Omega})]^3$.

Is $(1-x)^{\alpha} \log(1-x)$ a Sobolev function?

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