List questions from weak-derivatives

Published on 16 May 2020 - 21:24

45

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Limit of a function in $L^2(\mathbb{R}^N)$

Published on 18 May 2020 - 8:50

173

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Weak derivative in $L^1$

Published on 19 May 2020 - 15:00

264

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weak solution/variational method and the Lax Milgram Theorem

Published on 22 May 2020 - 10:29

939

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Must continuous $H^1(\mathbb{R}^2)$ function tend to zero at infinity?

Published on 23 May 2020 - 1:46

109

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weak solution / variational calculus

Published on 23 May 2020 - 8:32

76

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Two problems about Sobolev Space

Published on 13 Jun 2020 - 3:11

49

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Terms in the sum

Published on 26 Mar 2026 - 2:44

55

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Show that for all $w$, there is a unique $v$ with $\nabla\cdot v=0$ and $w=\nabla\wedge v$

Published on 17 Jun 2020 - 15:59

263

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Convergence of difference quotient in $L^{p}(\mathbb{R}^{n})$

Published on 20 Jun 2020 - 9:35

62

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If $\nabla\cdot u=0$ and $w=\operatorname{curl}u$, then $\int w=0$

Published on 20 Jun 2020 - 18:46

86

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If $u\in H_0^1(\Lambda,\mathbb R^2)\cap H^2(\Lambda,\mathbb R^2)$, is $\nabla^\perp\cdot\Delta u\in L^2(\Lambda)$?

Published on 22 Jun 2020 - 4:56

116

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If $u \in H^1(\Omega)$ with $\Delta u \in L^2(\Omega)^*$, is $u \in H^2(\Omega)$?

Published on 29 Jul 2020 - 19:07

435

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Is Laplacian of product of functions (one is smooth) square integrable?

Published on 06 Jul 2016 - 1:49

1.7k

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Is a weakly differentiable function differentiable almost everywhere?

Published on 06 Jul 2016 - 15:49

List Question

Show that a function $u$ has weak derivatives which satisfy the transport equation.

Limit of a function in $L^2(\mathbb{R}^N)$

Weak derivative in $L^1$

weak solution/variational method and the Lax Milgram Theorem

Must continuous $H^1(\mathbb{R}^2)$ function tend to zero at infinity?

weak solution / variational calculus

Two problems about Sobolev Space

Terms in the sum

Show that for all $w$, there is a unique $v$ with $\nabla\cdot v=0$ and $w=\nabla\wedge v$

Convergence of difference quotient in $L^{p}(\mathbb{R}^{n})$

If $\nabla\cdot u=0$ and $w=\operatorname{curl}u$, then $\int w=0$

If $u\in H_0^1(\Lambda,\mathbb R^2)\cap H^2(\Lambda,\mathbb R^2)$, is $\nabla^\perp\cdot\Delta u\in L^2(\Lambda)$?

If $u \in H^1(\Omega)$ with $\Delta u \in L^2(\Omega)^*$, is $u \in H^2(\Omega)$?

Is Laplacian of product of functions (one is smooth) square integrable?

Is a weakly differentiable function differentiable almost everywhere?

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