List questions from sobolev-spaces

521

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Is the space $C(0,1)$ dense in Sobolev space $H^2(0,1)$? And $C^\infty_c(\Omega) = C^\infty_0(\Omega)$?

Published on 11 Apr 2026 - 20:36

79

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Relation between $\limsup\;$ and Bounded Sequence

Published on 11 Apr 2026 - 18:08

42

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Finding $u_0 \in H_0^1(0,1)$ given $u'_0$

Published on 15 Apr 2026 - 17:19

324

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In Calculus of Variation: Problem applying variational principle theorem

Published on 11 Apr 2026 - 20:44

60

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real analysis - A bound for the product of two functions in $H^1$

Published on 12 Apr 2026 - 19:38

71

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Relation between $H^s$ for $0 \leq s \leq 1$ and Fourier decay

Published on 13 Apr 2026 - 12:04

59

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Are "boundary" conditions of a sequence of functions preserved in the limit?

Published on 11 Apr 2026 - 6:31

179

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Characterisation of Banach space $B$, given the RKHS of a Gaussian random variable in $B$.

Published on 25 Mar 2026 - 23:39

180

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Cauchy sequences on $L^p$ and $L^q$

Published on 14 Apr 2026 - 17:12

536

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Prove $H^1(\Omega)$ is complete given that $L_2(\Omega)$ is complete

Published on 28 Mar 2026 - 8:36

136

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Show that $\|u\|\leq \gamma \|\nabla u\|$.

Published on 17 Apr 2026 - 2:57

80

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Finding $\lambda$ for which $v(x)=|x|^\lambda\in L_2(\Omega), H^1(\Omega)$

Published on 12 Apr 2026 - 21:28

116

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Checking $v(x)=\log(-\log|x|^2)$ belongs to $H^1(\Omega)$

Published on 16 Apr 2026 - 2:47

169

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An example for $f\in H^1(\Omega)$ but not in $L^\infty(\Omega)$?

Published on 12 Apr 2026 - 1:48

463

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Proving $C_0^1(\Omega)$ is not dense in $H^1(\Omega)$.

Published on 13 Apr 2026 - 18:21

List Question

Is the space $C(0,1)$ dense in Sobolev space $H^2(0,1)$? And $C^\infty_c(\Omega) = C^\infty_0(\Omega)$?

Relation between $\limsup\;$ and Bounded Sequence

Finding $u_0 \in H_0^1(0,1)$ given $u'_0$

In Calculus of Variation: Problem applying variational principle theorem

real analysis - A bound for the product of two functions in $H^1$

Relation between $H^s$ for $0 \leq s \leq 1$ and Fourier decay

Are "boundary" conditions of a sequence of functions preserved in the limit?

Characterisation of Banach space $B$, given the RKHS of a Gaussian random variable in $B$.

Cauchy sequences on $L^p$ and $L^q$

Prove $H^1(\Omega)$ is complete given that $L_2(\Omega)$ is complete

Show that $\|u\|\leq \gamma \|\nabla u\|$.

Finding $\lambda$ for which $v(x)=|x|^\lambda\in L_2(\Omega), H^1(\Omega)$

Checking $v(x)=\log(-\log|x|^2)$ belongs to $H^1(\Omega)$

An example for $f\in H^1(\Omega)$ but not in $L^\infty(\Omega)$?

Proving $C_0^1(\Omega)$ is not dense in $H^1(\Omega)$.

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