List questions from weak-derivatives

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Uniqueness of Sturm-Liouville like problem

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64

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Existence of weak primitive

Published on 11 Oct 2023 - 21:35

90

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Extend these classic properties on the Fourier Transform using the $L^1$ approach.

Published on 17 Oct 2023 - 7:28

157

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Questions from Evans PDE problem 6.11

Published on 26 Mar 2026 - 19:24

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What does "Uniquely defined up to a set of measure 0" mean?

Published on 26 Oct 2023 - 12:47

241

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A clean proof of Chain rule for BV functions

Published on 04 Nov 2023 - 21:13

52

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If $u,v \in H^1_0(\Omega)$ and $\Delta u \in L^2(\Omega)$, can we write $\int_\Omega \nabla u \cdot \nabla v = \int_\Omega (-\Delta u)v $?

Published on 05 Nov 2023 - 12:58

22

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Weak derivative, constants infront of Dirac-delta

Published on 08 Nov 2023 - 13:07

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How do I find the weak derivative of this function?

Published on 13 Nov 2023 - 15:50

59

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Weak derivative of a function that is continuously differentiable except a finitely many points.

Published on 17 Nov 2023 - 20:52

54

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Proof of $|x|^{-\alpha} \in W^{1,p}(U)$

Published on 22 Nov 2023 - 16:26

40

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If $u(x) \in H^1(\mathbb R^n;\mathbb C)$, does the weak-derivative of $\frac{u(x)}{|u(x)|}$ exists?

Published on 23 Nov 2023 - 0:35

29

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Weak derivative of $|x|^{-\lambda}$.

Published on 24 Nov 2023 - 15:14

44

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What is the distributional derivative of this characteristic function on the square?

Published on 27 Nov 2023 - 13:21

List Question

Who is "the set of weakly differentiable functions"?

Uniqueness of Sturm-Liouville like problem

Existence of weak primitive

Extend these classic properties on the Fourier Transform using the $L^1$ approach.

Questions from Evans PDE problem 6.11

What does "Uniquely defined up to a set of measure 0" mean?

A clean proof of Chain rule for BV functions

If $u,v \in H^1_0(\Omega)$ and $\Delta u \in L^2(\Omega)$, can we write $\int_\Omega \nabla u \cdot \nabla v = \int_\Omega (-\Delta u)v $?

Weak derivative, constants infront of Dirac-delta

How do I find the weak derivative of this function?

Weak derivative of a function that is continuously differentiable except a finitely many points.

Proof of $|x|^{-\alpha} \in W^{1,p}(U)$

If $u(x) \in H^1(\mathbb R^n;\mathbb C)$, does the weak-derivative of $\frac{u(x)}{|u(x)|}$ exists?

Weak derivative of $|x|^{-\lambda}$.

What is the distributional derivative of this characteristic function on the square?

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