List questions from distribution-theory

Published on 08 May 2021 - 5:08

516

Views

Delta function singularity

Published on 11 Apr 2026 - 18:37

38

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Weak convergence of measures on the unit sphere $S^2$.

Published on 12 Apr 2026 - 8:33

170

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Is there a 'distributional antiderivative'?

Published on 11 Apr 2026 - 7:29

77

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Delta function limit definition in higher dimensions

Published on 09 Apr 2026 - 3:03

207

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Continuity equation, distributional derivative = usual derivative?

Published on 15 May 2021 - 14:22

72

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Distributional derivatives of euclidean norm

Published on 12 Apr 2026 - 9:48

41

Views

Proving $\delta \notin C_c$

Published on 17 May 2021 - 9:15

283

Views

Distributional derivative of multiple step function

Published on 08 Apr 2026 - 17:26

70

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Prove $u, \Delta u \in L^2(\mathbb{R}^n)$ then $u \in H^2(\mathbb{R}^n)$

Published on 18 May 2021 - 17:43

861

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Function which integrates to $0$ against test functions with mean $0$ is constant almost everywhere.

Published on 11 Apr 2026 - 15:46

124

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Product rule of distribution by multiplicating a $C^\infty$ function

Published on 20 May 2021 - 12:36

523

Views

Zero distributions

Published on 02 Apr 2026 - 2:47

109

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Determine $a$ and $p$ such that $u(x)=|x|^{-a}\in W^{1,p}(B_1(0))$

Published on 29 Mar 2026 - 4:41

59

Views

Determine $p$ such that $u(x,y)=1-\max\{|x|,|y|\}\in W^{1,p}((-1,1)\times(-1,1))$

Published on 29 Mar 2026 - 4:44

List Question

$-\Delta u+\epsilon \sin u=f$ has a unique solution in the sense of distribution

Delta function singularity

Weak convergence of measures on the unit sphere $S^2$.

Is there a 'distributional antiderivative'?

Delta function limit definition in higher dimensions

Continuity equation, distributional derivative = usual derivative?

Distributional derivatives of euclidean norm

Proving $\delta \notin C_c$

Distributional derivative of multiple step function

Prove $u, \Delta u \in L^2(\mathbb{R}^n)$ then $u \in H^2(\mathbb{R}^n)$

Function which integrates to $0$ against test functions with mean $0$ is constant almost everywhere.

Product rule of distribution by multiplicating a $C^\infty$ function

Zero distributions

Determine $a$ and $p$ such that $u(x)=|x|^{-a}\in W^{1,p}(B_1(0))$

Determine $p$ such that $u(x,y)=1-\max\{|x|,|y|\}\in W^{1,p}((-1,1)\times(-1,1))$

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