List questions from weak-derivatives

Published on 26 May 2021 - 17:23

37

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Non negative distributional derivative imply a.e. monotonicity

Published on 30 May 2021 - 11:01

62

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Write $D^{\alpha} f$ as a convolution

Published on 02 Jun 2021 - 21:03

104

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

Published on 03 Jun 2021 - 19:59

92

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Is the "Dirichlet Laplacian" an extension of $\Delta$ on $C^2(Ω)$ or only on $\{u\in C(\overline Ω)\cap C^2(Ω):\left.u\right|_{\partial\Omega}=0\}$?

Published on 28 Mar 2026 - 2:24

188

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Do convergence in $L^2$ and boundedness of gradients in $L^2$ imply convergence in $W^{1,2}$?

Published on 25 Jun 2021 - 23:39

25

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Stay $\|f\| \in W^{1,1}(0,T;\mathbb{R})$ provided $f \in W^{1,1}(0,T;H)$

Published on 27 Mar 2026 - 1:04

142

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Continuity of the $L^2$-norm with respect to a parameter

Published on 27 Jun 2021 - 12:38

125

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Inclusion of Sobolev spaces (from a proof by Bogachev - Krylov - Röckner - Shaposhnikov)

Published on 27 Jun 2021 - 19:52

240

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integration by parts in Sobolev space $W^{1,1}(\mathbb R^d)$

Published on 29 Jun 2021 - 15:54

500

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Show that D'Alembert solution gives distributional solution to the wave-equation

Published on 01 Jul 2021 - 19:09

107

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Can I extend a weak derivative to the whole $\mathbb R$?

Published on 09 Jul 2021 - 18:32

135

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Sobolev space of maps with higher dimensional target?

Published on 16 Jul 2021 - 14:50

94

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An continuity property in $W^{1,1}$

Published on 22 Jul 2021 - 9:40

81

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Generalized second derivative of a concave and piecewise $C^2$ function

Published on 25 Jul 2021 - 19:46

List Question

Gluing two functions from Sobolev spaces.

Non negative distributional derivative imply a.e. monotonicity

Write $D^{\alpha} f$ as a convolution

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

Is the "Dirichlet Laplacian" an extension of $\Delta$ on $C^2(Ω)$ or only on $\{u\in C(\overline Ω)\cap C^2(Ω):\left.u\right|_{\partial\Omega}=0\}$?

Do convergence in $L^2$ and boundedness of gradients in $L^2$ imply convergence in $W^{1,2}$?

Stay $\|f\| \in W^{1,1}(0,T;\mathbb{R})$ provided $f \in W^{1,1}(0,T;H)$

Continuity of the $L^2$-norm with respect to a parameter

Inclusion of Sobolev spaces (from a proof by Bogachev - Krylov - Röckner - Shaposhnikov)

integration by parts in Sobolev space $W^{1,1}(\mathbb R^d)$

Show that D'Alembert solution gives distributional solution to the wave-equation

Can I extend a weak derivative to the whole $\mathbb R$?

Sobolev space of maps with higher dimensional target?

An continuity property in $W^{1,1}$

Generalized second derivative of a concave and piecewise $C^2$ function

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