List questions from weak-derivatives

Published on 11 Apr 2026 - 12:20

650

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Weak derivative and Locally summable functions

Published on 13 Apr 2026 - 19:19

46

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$u,v \in W^{1,2}(\Bbb{R})$, then $\int_\Bbb{R}{uv'}dx=-\int_\Bbb{R}{u'v}dx$

Published on 16 Apr 2026 - 14:35

144

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Elliptic PDE- solution in weak sense

Published on 11 Apr 2026 - 13:14

98

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Is there a Sobolev map $\mathbb{R}^4 \to \mathbb{R}^4$ whose differential zig-zags between a value and its negative?

Published on 11 Apr 2026 - 11:07

132

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Is the function $f(x,y)=y \cdot \text{sign}(x)$ Sobolev?

Published on 15 Apr 2026 - 11:37

686

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Is weak derivative a bounded operator from $H^k(\mathbb{R}^n)$ to $L^2(\mathbb{R}^n)$?

Published on 11 Apr 2026 - 1:29

230

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The restriction of a variable in a Sobolev function is a.e. Sobolev

Published on 06 May 2026 - 7:41

717

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Solve $xu = 0$ in the sense of distribution

Published on 12 Apr 2026 - 9:26

2.9k

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Weak derivative of absolute value of function

Published on 17 Apr 2026 - 6:40

276

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How is the differential of a Sobolev function on a manifold regarded as an a.e. defined section of $T^*M$?

Published on 13 Apr 2026 - 5:40

28

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Locally closed in the sense of distributions implies closed?

Published on 13 Apr 2026 - 14:07

315

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weak solution of PDE and apply Lax-Milgram

Published on 12 Apr 2026 - 23:48

1k

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Sobolev spaces for vector-valued functions

Published on 16 Apr 2026 - 13:53

420

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Weak derivative

Published on 30 Apr 2026 - 13:55

List Question

Convergence of energy estimates of weak solutions.

Weak derivative and Locally summable functions

$u,v \in W^{1,2}(\Bbb{R})$, then $\int_\Bbb{R}{uv'}dx=-\int_\Bbb{R}{u'v}dx$

Elliptic PDE- solution in weak sense

Is there a Sobolev map $\mathbb{R}^4 \to \mathbb{R}^4$ whose differential zig-zags between a value and its negative?

Is the function $f(x,y)=y \cdot \text{sign}(x)$ Sobolev?

Is weak derivative a bounded operator from $H^k(\mathbb{R}^n)$ to $L^2(\mathbb{R}^n)$?

The restriction of a variable in a Sobolev function is a.e. Sobolev

Solve $xu = 0$ in the sense of distribution

Weak derivative of absolute value of function

How is the differential of a Sobolev function on a manifold regarded as an a.e. defined section of $T^*M$?

Locally closed in the sense of distributions implies closed?

weak solution of PDE and apply Lax-Milgram

Sobolev spaces for vector-valued functions

Weak derivative

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