List questions from sobolev-spaces

Published on 02 Nov 2019 - 19:02

87

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If $\int_U |Du|^2 dx + \int_{\partial U}u^2 dx < \infty$ is $\int_U |u|^2 dx < \infty$?

Published on 04 Nov 2019 - 8:58

188

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is $H^{1}\left(\Omega\right)\cap L^{\infty}\left(\Omega\right)$ closed in $H^{1}\left(\Omega\right)$?

Published on 04 Nov 2019 - 20:01

241

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Generalized definition of the Green Formula (In Sobolev Spaces)

Published on 23 Feb 2026 - 8:33

109

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Exact solution $\int_0^1 u'v'=v(1/2)$

Published on 26 Mar 2026 - 2:54

31

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Is $\left\{ u\in H^{1}\left(\Omega\right)\left|\,a<u\left(x\right) <b\:\text{a.e.}\right.\right\}$ open in $H^1(\Omega)$

Published on 07 Nov 2019 - 21:07

324

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Compact Embeddings

Published on 29 Mar 2026 - 12:13

67

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$u \in W^{1,p} (U)$ Implies $u^{+}, u^{-} \in W^{1,p}(U)$ for $U \subseteq \mathbb{R}^N$ Bounded (Evans, Chapter 5, Exercise 18)

Published on 10 Nov 2019 - 11:24

142

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Weak limit of gradient of functions

Published on 11 Nov 2019 - 3:02

41

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A density problem in Sobolev space?

Published on 13 Nov 2019 - 5:21

51

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Fixed Point Theorem in Topological vector spaces

Published on 27 Mar 2026 - 9:37

114

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About extension on Sobolev space

Published on 15 Nov 2019 - 19:56

332

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Variational formulation Poisson equation (1d FEM)

Published on 25 Mar 2026 - 17:38

266

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Density of $C^{\infty}(I) \cap W^{1,\infty}(I)$ in $W^{1,\infty}(I)$

Published on 20 Nov 2019 - 16:10

190

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A funny exercise with bounded Lipschitz domain and Sobolev spaces

Published on 20 Nov 2019 - 16:28

List Question

$u_n\rightarrow u$ and $\nabla u_n\rightarrow g$ implies $g=\nabla u$?

If $\int_U |Du|^2 dx + \int_{\partial U}u^2 dx < \infty$ is $\int_U |u|^2 dx < \infty$?

is $H^{1}\left(\Omega\right)\cap L^{\infty}\left(\Omega\right)$ closed in $H^{1}\left(\Omega\right)$?

Generalized definition of the Green Formula (In Sobolev Spaces)

Exact solution $\int_0^1 u'v'=v(1/2)$

Is $\left\{ u\in H^{1}\left(\Omega\right)\left|\,a<u\left(x\right) <b\:\text{a.e.}\right.\right\}$ open in $H^1(\Omega)$

Compact Embeddings

$u \in W^{1,p} (U)$ Implies $u^{+}, u^{-} \in W^{1,p}(U)$ for $U \subseteq \mathbb{R}^N$ Bounded (Evans, Chapter 5, Exercise 18)

Weak limit of gradient of functions

A density problem in Sobolev space?

Fixed Point Theorem in Topological vector spaces

About extension on Sobolev space

Variational formulation Poisson equation (1d FEM)

Density of $C^{\infty}(I) \cap W^{1,\infty}(I)$ in $W^{1,\infty}(I)$

A funny exercise with bounded Lipschitz domain and Sobolev spaces

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