List questions from weak-derivatives

Published on 10 Jul 2016 - 21:59

100

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If $p,q$ are distributions with $\partial_ip=\partial_iq$, then $p=q$

Published on 11 Jul 2016 - 18:43

5.3k

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Why is it useful to show the existence and uniqueness of solution for a PDE?

Published on 26 Mar 2026 - 6:21

42

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Showing that $|u|$ is absolutely continuous for $u \in C^1(\overline{\Omega})$

Published on 12 Jul 2016 - 19:01

242

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Distribution Convergence in PDE theory

Published on 13 Jul 2016 - 20:28

427

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Has the distributional Laplacian $\Delta f:C_c^\infty(\Omega)'\to C_c^\infty(\Omega)'$ a unique extension in $H_0^1(\Omega)'$?

Published on 14 Jul 2016 - 10:04

1.6k

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Relationship between the distributional Laplacian and the weak Laplacian

Published on 15 Jul 2016 - 9:56

1.3k

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Weak derivative of maximum

Published on 26 Jul 2016 - 10:19

1.1k

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Bounded difference quotient implies weakly differentiable.

Published on 30 Jul 2016 - 18:01

52

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If $u:[0,\infty)\times\mathcal V\to\mathbb R^d$ is divergence-free, then $\partial u/\partial t$ is divergence-free too

Published on 01 Aug 2016 - 18:43

1k

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Distributional derivative of $x^{-1/2} 1_{x \in [0,1]}$

Published on 02 Aug 2016 - 15:14

45

Views

Apparent paradox for second order derivatives

Published on 03 Aug 2016 - 18:38

464

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Weak Derivative of a function given by an integral

Published on 25 Mar 2026 - 12:46

70

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Arguing a heuristic solution to a linear PDE, in weak formulation

Published on 10 Aug 2016 - 9:15

102

Views

Conclude $u\frac{\partial v}{\partial x_i}\in L^2(\Lambda)$ for all $u,v\in H_0^1(\Lambda)$ from the Sobolev embedding theorem

Published on 11 Aug 2016 - 15:14

List Question

What is the divergence of a distribution?

If $p,q$ are distributions with $\partial_ip=\partial_iq$, then $p=q$

Why is it useful to show the existence and uniqueness of solution for a PDE?

Showing that $|u|$ is absolutely continuous for $u \in C^1(\overline{\Omega})$

Distribution Convergence in PDE theory

Has the distributional Laplacian $\Delta f:C_c^\infty(\Omega)'\to C_c^\infty(\Omega)'$ a unique extension in $H_0^1(\Omega)'$?

Relationship between the distributional Laplacian and the weak Laplacian

Weak derivative of maximum

Bounded difference quotient implies weakly differentiable.

If $u:[0,\infty)\times\mathcal V\to\mathbb R^d$ is divergence-free, then $\partial u/\partial t$ is divergence-free too

Distributional derivative of $x^{-1/2} 1_{x \in [0,1]}$

Apparent paradox for second order derivatives

Weak Derivative of a function given by an integral

Arguing a heuristic solution to a linear PDE, in weak formulation

Conclude $u\frac{\partial v}{\partial x_i}\in L^2(\Lambda)$ for all $u,v\in H_0^1(\Lambda)$ from the Sobolev embedding theorem

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