List questions from sobolev-spaces

Published on 22 Mar 2026 - 5:30

118

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The norm of a distribution (generalized function) in a Sobolev Spaces involving time.

Published on 29 Dec 2019 - 21:56

106

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How to interpret $|\nabla u|$ when using distributions?

Published on 29 Mar 2026 - 15:20

218

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Norm in Sobolev space $H^m(\mathbb R^n)$ is finite: need I really prove this?

Published on 30 Dec 2019 - 12:25

49

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What properties of $A:H^{-1/2}([0,2\pi])\to H^{1/2}([0,2\pi])$ allow us to bound the Sobolev operator norm of $A$ by the $L^2$ operator norm?

Published on 27 Mar 2026 - 13:01

139

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Is the weak derivative invertible from $H^1(\mathbb{R})\to L^2(\mathbb{R})$?

Published on 30 Dec 2019 - 23:10

54

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The wave equation, Fourier formula

Published on 28 Mar 2026 - 22:30

50

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Elements in fractional Sobolev space

Published on 27 Mar 2026 - 11:26

37

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Why $\|u\|_{L^{2}}\|v\|_{L^{2}}+\|v'\|_{L^{2}}+\|u'\|_{L^{2}}≤\|v\|_{H^{1}}\|u\|_{H^{1}}$

Published on 26 Mar 2026 - 16:06

911

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Weak convergence in the space of tempered distributions and weighted Sobolev spaces

Published on 26 Mar 2026 - 0:53

625

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Why the Heaviside distribution $H$ doesn't belong to any Sobolev space $H^{s}(\mathbb{R})$

Published on 29 Mar 2026 - 16:50

518

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Trying to use Lax-Milgram to solve a PDE

Published on 29 Mar 2026 - 16:02

179

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Properties of the adjoint of multiplication on Sobolev space

Published on 08 Jan 2020 - 20:00

21

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Convergence of "samples" of a function in Lp

Published on 09 Jan 2020 - 16:26

38

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$\ \|u\|_{H^{s}} \leq\|u\|_{s_{0}}^{\alpha}\|u\|_{s_{1}}^{1-\alpha}, \quad \forall u \in H^{s_{1}}\left(\mathbb{R}^{n}\right) $

Published on 09 Jan 2020 - 22:58

List Question

Existence of trace operator in$ W^{s,p} (D)$

The norm of a distribution (generalized function) in a Sobolev Spaces involving time.

How to interpret $|\nabla u|$ when using distributions?

Norm in Sobolev space $H^m(\mathbb R^n)$ is finite: need I really prove this?

What properties of $A:H^{-1/2}([0,2\pi])\to H^{1/2}([0,2\pi])$ allow us to bound the Sobolev operator norm of $A$ by the $L^2$ operator norm?

Is the weak derivative invertible from $H^1(\mathbb{R})\to L^2(\mathbb{R})$?

The wave equation, Fourier formula

Elements in fractional Sobolev space

Why $\|u\|_{L^{2}}\|v\|_{L^{2}}+\|v'\|_{L^{2}}+\|u'\|_{L^{2}}≤\|v\|_{H^{1}}\|u\|_{H^{1}}$

Weak convergence in the space of tempered distributions and weighted Sobolev spaces

Why the Heaviside distribution $H$ doesn't belong to any Sobolev space $H^{s}(\mathbb{R})$

Trying to use Lax-Milgram to solve a PDE

Properties of the adjoint of multiplication on Sobolev space

Convergence of "samples" of a function in Lp

$\ \|u\|_{H^{s}} \leq\|u\|_{s_{0}}^{\alpha}\|u\|_{s_{1}}^{1-\alpha}, \quad \forall u \in H^{s_{1}}\left(\mathbb{R}^{n}\right) $

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