List questions from sobolev-spaces

Published on 25 Apr 2026 - 21:27

175

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$W^{1,p}_0 (\mathbb{R}^n) = W^{1,p}(\mathbb{R}^n) $

Published on 17 Apr 2026 - 6:40

253

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Show that there exists a unique weak solution $(u, p)$ such that $-\Delta u + p = f$

Published on 16 Apr 2026 - 5:11

69

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Embedding of $W^{1,\infty}(\Omega)$ into $W^{1,1}(\Omega)$ when $\Omega$ is bounded

Published on 14 Apr 2026 - 17:48

76

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Unusual Sobolev Chain rule

Published on 11 Apr 2026 - 10:17

290

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Sobolev spaces involving time

Published on 17 Apr 2026 - 5:38

68

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Trace of $W^{k,p}(\Omega)$ space is $W^{k-1/p,p}(\partial \Omega)$

Published on 11 Apr 2026 - 1:43

63

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Implication of Sobolev inequality

Published on 13 Apr 2026 - 16:49

132

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Requirements on function for Fourier Transform on compact subset of $\mathbb{R}^d$

Published on 13 Apr 2026 - 10:52

94

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Poincaré inequality on manifold

Published on 14 Apr 2026 - 0:02

96

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Why compact support assumption is necessary for the following proof: that $Dv_\epsilon = (Dv)_\epsilon$

Published on 16 Apr 2026 - 20:18

47

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Prove the following inequality for $p\|v\|_p^{p-1}\|v'\|_p \le C^p \|v\|_{W^{1,p}}$

Published on 16 Apr 2026 - 1:28

50

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A question about convolution.

Published on 09 Apr 2026 - 3:39

83

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Prove that convergence subsequence given by the compact inclusion $W^{1,p}(I) \subset C(\bar{I})$ convege to some function in $W^{1,p}(I)$

Published on 14 Apr 2026 - 16:19

379

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Helley's selection theorem

Published on 12 Apr 2026 - 19:45

List Question

Does this Weighted Lp bound my Sobolev-esque Fourier Space?

$W^{1,p}_0 (\mathbb{R}^n) = W^{1,p}(\mathbb{R}^n) $

Show that there exists a unique weak solution $(u, p)$ such that $-\Delta u + p = f$

Embedding of $W^{1,\infty}(\Omega)$ into $W^{1,1}(\Omega)$ when $\Omega$ is bounded

Unusual Sobolev Chain rule

Sobolev spaces involving time

Trace of $W^{k,p}(\Omega)$ space is $W^{k-1/p,p}(\partial \Omega)$

Implication of Sobolev inequality

Requirements on function for Fourier Transform on compact subset of $\mathbb{R}^d$

Poincaré inequality on manifold

Why compact support assumption is necessary for the following proof: that $Dv_\epsilon = (Dv)_\epsilon$

Prove the following inequality for $p\|v\|_p^{p-1}\|v'\|_p \le C^p \|v\|_{W^{1,p}}$

A question about convolution.

Prove that convergence subsequence given by the compact inclusion $W^{1,p}(I) \subset C(\bar{I})$ convege to some function in $W^{1,p}(I)$

Helley's selection theorem

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