List questions from sobolev-spaces

Published on 10 Sep 2016 - 0:31

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Equivalent conditions of weak differentiability

Published on 26 Mar 2026 - 14:18

362

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Does dense embedding say anything about the embedding of their dual space?

Published on 10 Sep 2016 - 17:42

43

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$\int_{\Omega} D^{m} (|u|^{p-2}u) D^{m} u' dx\leq \|D^{m} u\|_{2}^{p-1}. \| D^{m} u'\|_{2}$?

Published on 10 Sep 2016 - 20:02

41

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If $u\in C^{1,\:2}([0,T]\times\Omega,\mathbb R^d)$, what can we say about the Fréchet differentiability of $t\mapsto u(t,\;\cdot\;)$?

Published on 25 Mar 2026 - 23:13

397

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Reference request: definition of $H^{1/2}(\partial\Omega)$.

Published on 11 Sep 2016 - 1:55

129

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Understanding Sobolev spaces

Published on 12 Sep 2016 - 2:17

54

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If $u\in H_{0}^{m}(\Omega)$ then $\|D^{m} f(u)\|_{2}<+\infty $?

Published on 12 Sep 2016 - 10:09

274

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Is a constant function in a Sobolev space between manifolds always $C^\infty$?

Published on 12 Sep 2016 - 18:23

151

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$ \Delta p=0$ and $(\nabla p)\cdot \nu\big|_{\partial\Omega}=0 $ in $H^1(\Omega)$ implies $p$ is a constant

Published on 31 Mar 2026 - 7:09

288

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Counterexample Sobolev inequality?

Published on 15 Sep 2016 - 9:15

55

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Relation between weighted Sobolev space and ^$L^{1}(\mathbb{R}^{N})$

Published on 16 Sep 2016 - 1:40

132

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How to show translation generates weak convergence?

Published on 18 Sep 2016 - 10:06

235

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Smooth domain, minimally smooth domain, extension opearors

Published on 19 Sep 2016 - 0:27

161

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On the continuous Sobolev embedding, smooth domain

Published on 19 Sep 2016 - 2:38

List Question

Prove an inf-sup condition on usual spaces

Equivalent conditions of weak differentiability

Does dense embedding say anything about the embedding of their dual space?

$\int_{\Omega} D^{m} (|u|^{p-2}u) D^{m} u' dx\leq \|D^{m} u\|_{2}^{p-1}. \| D^{m} u'\|_{2}$?

If $u\in C^{1,\:2}([0,T]\times\Omega,\mathbb R^d)$, what can we say about the Fréchet differentiability of $t\mapsto u(t,\;\cdot\;)$?

Reference request: definition of $H^{1/2}(\partial\Omega)$.

Understanding Sobolev spaces

If $u\in H_{0}^{m}(\Omega)$ then $\|D^{m} f(u)\|_{2}<+\infty $?

Is a constant function in a Sobolev space between manifolds always $C^\infty$?

$ \Delta p=0$ and $(\nabla p)\cdot \nu\big|_{\partial\Omega}=0 $ in $H^1(\Omega)$ implies $p$ is a constant

Counterexample Sobolev inequality?

Relation between weighted Sobolev space and ^$L^{1}(\mathbb{R}^{N})$

How to show translation generates weak convergence?

Smooth domain, minimally smooth domain, extension opearors

On the continuous Sobolev embedding, smooth domain

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