List questions from sobolev-spaces

Published on 09 Apr 2026 - 15:17

88

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a function defined only upto a set of measure zero

Published on 14 Apr 2026 - 11:56

39

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$||F(u)||_{H^k}\leq C_k||u||_{L^\infty}(1+||u||_{H^k})$

Published on 12 Apr 2026 - 0:50

79

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First derivative of cut-off function

Published on 13 Apr 2026 - 12:16

60

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Is the function space $X=\{u \in H^1(\Omega) : \text{$u$ is continuous at $0$}\}$ complete?

Published on 14 Apr 2026 - 0:33

202

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Best Constant for Sobolev-Type Inequality

Published on 13 Apr 2026 - 22:20

89

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Unitarity of $e^{-it\Delta }$ as a map on Sobolev spaces.

Published on 12 Apr 2026 - 0:32

150

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Show that Fourier transform is isomorphism between $H^r_m (\mathbb R)$ and $H^m_r (\mathbb R)$.

Published on 14 Apr 2026 - 10:20

218

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Right inverse of trace operator

Published on 14 May 2026 - 10:39

521

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Integral of the usual mollifier function: finding its necessary constant

Published on 11 Apr 2026 - 3:56

54

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How to prove that extensions of Sobolev functions if Sobolev?

Published on 10 Apr 2026 - 17:01

515

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Dual of the Sobolev space

Published on 11 Apr 2026 - 20:19

83

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How to show $u_n(x)=\sum_{k=1}^n \frac{1}{2^k}\vert x-r_k \vert^{-\alpha}$ is a Cauchy sequence in $W^{1,p}(U)$?

Published on 17 Apr 2026 - 15:33

53

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Sobolev function in $X = W_0^{1,2}(\Omega) \cap W^{2,2}(\Omega) $

Published on 14 Apr 2026 - 19:24

68

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Uniquess of Lagrange Multiplier in Calculus of Variations

Published on 11 Apr 2026 - 21:34

List Question

Do the sum of some function belong to specific spaces

a function defined only upto a set of measure zero

$||F(u)||_{H^k}\leq C_k||u||_{L^\infty}(1+||u||_{H^k})$

First derivative of cut-off function

Is the function space $X=\{u \in H^1(\Omega) : \text{$u$ is continuous at $0$}\}$ complete?

Best Constant for Sobolev-Type Inequality

Unitarity of $e^{-it\Delta }$ as a map on Sobolev spaces.

Show that Fourier transform is isomorphism between $H^r_m (\mathbb R)$ and $H^m_r (\mathbb R)$.

Right inverse of trace operator

Integral of the usual mollifier function: finding its necessary constant

How to prove that extensions of Sobolev functions if Sobolev?

Dual of the Sobolev space

How to show $u_n(x)=\sum_{k=1}^n \frac{1}{2^k}\vert x-r_k \vert^{-\alpha}$ is a Cauchy sequence in $W^{1,p}(U)$?

Sobolev function in $X = W_0^{1,2}(\Omega) \cap W^{2,2}(\Omega) $

Uniquess of Lagrange Multiplier in Calculus of Variations

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