List questions from sobolev-spaces

Published on 18 Jan 2016 - 13:29

544

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Relation between seminorm of Sobolev space and $L^2$ norm

Published on 18 Jan 2016 - 13:44

75

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What is the purpose of the requirement on mollification radius?

Published on 03 Apr 2026 - 21:49

16.9k

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cutoff function vs mollifiers

Published on 29 Mar 2026 - 4:11

810

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What is the divergence $\operatorname{div}u$ of a $L^2(\Omega)^d$ function $u$?

Published on 04 Apr 2026 - 7:26

420

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Intuition for Sobolev spaces $H^{\frac{1}{2}}$ and $H^{-\frac{1}{2}}$

Published on 21 Jan 2016 - 15:32

49

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Minimizing point for $L^2$ distance.

Published on 21 Jan 2016 - 20:08

33

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Convergence rate of functions

Published on 21 Jan 2016 - 21:31

46

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Existence of $u\in C^1[0,1]$ such that $u\notin H^1(0,1)$

Published on 22 Jan 2016 - 15:29

1.1k

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Does the weak divergence exist for each $\mathcal L^2(\Omega;\mathbb R^d)$-function?

Published on 27 Mar 2026 - 20:19

246

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Is it true that $C_1\|\Delta u \|_{0,\Omega} \leq |u|_{2,\Omega} \leq C_2\|\Delta u \|_{0,\Omega}$ for a bounded domain $\Omega\subset\mathbb{R}^2$?

Published on 12 Apr 2026 - 23:45

644

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Computing the inverse of Laplacian operator.

Published on 31 Mar 2026 - 14:12

263

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Estimate of a Fourier Multiplier Operator

Published on 08 Apr 2026 - 21:00

59

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What is the "minimal" space one can embed $W^{1,p}$ into?

Published on 27 Jan 2016 - 15:18

42

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Convergence of the series $\sum_{k=1}^{\infty} \frac{1}{2^k} |x-y_k|^{-\alpha}$

Published on 27 Mar 2026 - 15:19

List Question

Using Nash inequality to derive an inequality (from proof in paper)

Relation between seminorm of Sobolev space and $L^2$ norm

What is the purpose of the requirement on mollification radius?

cutoff function vs mollifiers

What is the divergence $\operatorname{div}u$ of a $L^2(\Omega)^d$ function $u$?

Intuition for Sobolev spaces $H^{\frac{1}{2}}$ and $H^{-\frac{1}{2}}$

Minimizing point for $L^2$ distance.

Convergence rate of functions

Existence of $u\in C^1[0,1]$ such that $u\notin H^1(0,1)$

Does the weak divergence exist for each $\mathcal L^2(\Omega;\mathbb R^d)$-function?

Is it true that $C_1\|\Delta u \|_{0,\Omega} \leq |u|_{2,\Omega} \leq C_2\|\Delta u \|_{0,\Omega}$ for a bounded domain $\Omega\subset\mathbb{R}^2$?

Computing the inverse of Laplacian operator.

Estimate of a Fourier Multiplier Operator

What is the "minimal" space one can embed $W^{1,p}$ into?

Convergence of the series $\sum_{k=1}^{\infty} \frac{1}{2^k} |x-y_k|^{-\alpha}$

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