List questions from weak-derivatives

Published on 28 Sep 2018 - 17:16

647

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Weak derivative and Locally summable functions

Published on 16 Oct 2018 - 13:27

43

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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 17 Oct 2018 - 15:00

142

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Elliptic PDE- solution in weak sense

Published on 25 Mar 2026 - 5:59

95

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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 01 Nov 2018 - 9:56

129

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

Published on 03 Nov 2018 - 15:22

683

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

Published on 03 Nov 2018 - 15:40

222

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

Published on 22 Mar 2026 - 3:46

714

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Solve $xu = 0$ in the sense of distribution

Published on 07 Nov 2018 - 8:54

2.9k

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Weak derivative of absolute value of function

Published on 10 Nov 2018 - 3:30

273

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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 12 Nov 2018 - 13:45

25

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Locally closed in the sense of distributions implies closed?

Published on 20 Nov 2018 - 11:06

312

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weak solution of PDE and apply Lax-Milgram

Published on 25 Nov 2018 - 23:34

1k

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Sobolev spaces for vector-valued functions

Published on 26 Nov 2018 - 6:45

415

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Weak derivative

Published on 12 Dec 2018 - 13:35

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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