List questions from sobolev-spaces

Published on 14 Apr 2026 - 2:25

80

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Is it true that $f\in L^1(\mathbb R)$ and $(1+x^2)f''\in L^1(\mathbb R)$ imply $xf'\in L^1(\mathbb R)$?

Published on 15 Apr 2026 - 18:08

89

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A detailed demostration of $Du=0\quad \mbox{a.e }\Longrightarrow u\equiv C\quad\mbox{a.e}$

Published on 16 Apr 2026 - 15:49

630

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Can you always bound the derivative of a Sobolev norm by a higher Sobolev norm in $\mathbb R$ and $\mathbb R^n$?

Published on 14 Apr 2026 - 14:43

26

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Extending a solution of a differential operator in a sobolev space

Published on 09 Apr 2026 - 13:35

319

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Generalization of Cauchy-Schwarz/Hölder inequality

Published on 17 Apr 2026 - 6:34

165

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$W_0^{1,p}(\Omega)\neq W^{1,p}(\Omega)$

Published on 16 Apr 2026 - 4:49

76

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Inequalities of $H^s$-norm, $(s=0,1)$ $\|v\|^2_s \leq \sqrt2 \|v\|_{s-1}\|v\|_{s+1}$ when $v\in H^{s+1}(\Omega) \cap H_0^1(\Omega)$

Published on 14 Apr 2026 - 22:40

123

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Find $p$ such that the integral is finite

Published on 15 Apr 2026 - 17:07

76

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Regularity of the law of a random variable

Published on 13 Apr 2026 - 19:54

171

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Poincaré inequality, bounded norm

Published on 13 Apr 2026 - 1:57

212

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Diffeomorphism and bounds on Sobolev $H^1$ norms

Published on 12 Apr 2026 - 6:35

50

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Question about the approximation argument in the Logarithmic Sobolev inequality

Published on 11 Apr 2026 - 23:13

48

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Laplace Operator notation

Published on 13 Apr 2026 - 14:59

401

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Poincaré’s inequality for a bounded open set in Brezis' book

Published on 14 Apr 2026 - 7:37

List Question

Integration by parts $H^2(\mathbb{R})$

Is it true that $f\in L^1(\mathbb R)$ and $(1+x^2)f''\in L^1(\mathbb R)$ imply $xf'\in L^1(\mathbb R)$?

A detailed demostration of $Du=0\quad \mbox{a.e }\Longrightarrow u\equiv C\quad\mbox{a.e}$

Can you always bound the derivative of a Sobolev norm by a higher Sobolev norm in $\mathbb R$ and $\mathbb R^n$?

Extending a solution of a differential operator in a sobolev space

Generalization of Cauchy-Schwarz/Hölder inequality

$W_0^{1,p}(\Omega)\neq W^{1,p}(\Omega)$

Inequalities of $H^s$-norm, $(s=0,1)$ $\|v\|^2_s \leq \sqrt2 \|v\|_{s-1}\|v\|_{s+1}$ when $v\in H^{s+1}(\Omega) \cap H_0^1(\Omega)$

Find $p$ such that the integral is finite

Regularity of the law of a random variable

Poincaré inequality, bounded norm

Diffeomorphism and bounds on Sobolev $H^1$ norms

Question about the approximation argument in the Logarithmic Sobolev inequality

Laplace Operator notation

Poincaré’s inequality for a bounded open set in Brezis' book

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