List questions from weak-derivatives

Published on 27 Feb 2016 - 23:29

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Identity having to do with weak derivative

Published on 07 Mar 2016 - 16:24

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Solve the differential equation $x^2u'=0$ in the sense of distributions

Published on 14 Mar 2016 - 4:19

1.1k

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Distributional solution of the heat equation

Published on 14 Mar 2016 - 20:09

328

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If $u_n \rightharpoonup u$ in $H_0^1(\Omega)$, what can we say about $\{\nabla u_n\}$?

Published on 22 Mar 2016 - 0:20

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Definition of weak time derivative

Published on 26 Mar 2026 - 14:20

70

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Constant weak differentaible functions?!

Published on 29 Mar 2016 - 17:57

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Integral of a weak derivative

Published on 26 Mar 2026 - 14:20

155

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Find a discontinuous function from $\mathbb R^n \to \mathbb R$ which is weakly differentiable.

Published on 03 Apr 2016 - 23:35

69

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Sobolev space and norms

Published on 14 Apr 2016 - 12:11

369

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Show that if $\,u \in W^{1,p}\left(I\right) \bigcap C_c\left(I\right)$, then $\,u \in W_{0}^{1,p}\left(I\right)$.

Published on 16 Apr 2016 - 11:21

1.9k

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Distributional derivatives

Published on 16 Apr 2016 - 20:55

90

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Can we show that each element of the Sobolev space $H^k(D)$, with $D\subseteq\mathbb R^d$ being a bounded domain, has a continuous representative?

Published on 18 Apr 2016 - 15:41

231

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Product of two $W^{1,p}_0$ functions

Published on 18 Apr 2016 - 20:41

287

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Integral of weak derivative is finite

Published on 19 Apr 2016 - 19:25

List Question

How can we apply the formula?

Identity having to do with weak derivative

Solve the differential equation $x^2u'=0$ in the sense of distributions

Distributional solution of the heat equation

If $u_n \rightharpoonup u$ in $H_0^1(\Omega)$, what can we say about $\{\nabla u_n\}$?

Definition of weak time derivative

Constant weak differentaible functions?!

Integral of a weak derivative

Find a discontinuous function from $\mathbb R^n \to \mathbb R$ which is weakly differentiable.

Sobolev space and norms

Show that if $\,u \in W^{1,p}\left(I\right) \bigcap C_c\left(I\right)$, then $\,u \in W_{0}^{1,p}\left(I\right)$.

Distributional derivatives

Can we show that each element of the Sobolev space $H^k(D)$, with $D\subseteq\mathbb R^d$ being a bounded domain, has a continuous representative?

Product of two $W^{1,p}_0$ functions

Integral of weak derivative is finite

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