List questions from sobolev-spaces

Published on 24 Mar 2026 - 21:22

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L2-Norm of Gradient?

Published on 25 Mar 2026 - 10:52

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Is there any continuous function in the Sobolev space $\mathcal{H}^k(\mathbb{R}^d)$ but not in $\mathcal{H}^{d/2}(\mathbb{R}^d)$

Published on 22 Feb 2018 - 15:16

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An estimate of harmonic function

Published on 25 Mar 2026 - 12:31

69

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Young's inequality with duality bracket

Published on 20 Mar 2026 - 5:03

457

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smooth envelope of the convex function

Published on 26 Feb 2018 - 9:34

75

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Why is $W^{1,p}(\Omega;S)$ weakly closed in $W^{1,p}(\Omega;\mathbb R^N)$ for a compact set $S$?

Published on 27 Feb 2018 - 18:29

29

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Projector-like operator $P:H^1(\Omega)\longrightarrow P_k(\Omega)$ such that $\|Pv\|\geq C\|v\|$

Published on 27 Feb 2018 - 22:24

80

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Sobolev spaces on different domains

Published on 22 Mar 2026 - 19:03

207

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Why the generalized derivatives defined? Why was it needed?

Published on 17 Mar 2026 - 15:49

182

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Convergence by Vitali's theorem?

Published on 01 Mar 2018 - 20:14

262

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On Sobolev space $W^{2,2}$, is the inner product of the derivative of a function and the function itself zero?

Published on 01 Mar 2018 - 20:46

130

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Evans-Gariepy proof of $f\in W^{1,\infty}_\text{loc}(U)$ iff $f$ is locally Lipschitz continuous in $U$

Published on 01 Mar 2018 - 22:02

80

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Operator defined on periodic-distribution sobolev space

Published on 25 Mar 2026 - 4:35

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Sobolev space embeded in to $L^\infty$

Published on 02 Mar 2018 - 3:33

List Question

About a Sobolev function that admits a Lipschitz representative

L2-Norm of Gradient?

Is there any continuous function in the Sobolev space $\mathcal{H}^k(\mathbb{R}^d)$ but not in $\mathcal{H}^{d/2}(\mathbb{R}^d)$

An estimate of harmonic function

Young's inequality with duality bracket

smooth envelope of the convex function

Why is $W^{1,p}(\Omega;S)$ weakly closed in $W^{1,p}(\Omega;\mathbb R^N)$ for a compact set $S$?

Projector-like operator $P:H^1(\Omega)\longrightarrow P_k(\Omega)$ such that $\|Pv\|\geq C\|v\|$

Sobolev spaces on different domains

Why the generalized derivatives defined? Why was it needed?

Convergence by Vitali's theorem?

On Sobolev space $W^{2,2}$, is the inner product of the derivative of a function and the function itself zero?

Evans-Gariepy proof of $f\in W^{1,\infty}_\text{loc}(U)$ iff $f$ is locally Lipschitz continuous in $U$

Operator defined on periodic-distribution sobolev space

Sobolev space embeded in to $L^\infty$

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