List questions from sobolev-spaces

Published on 27 Mar 2026 - 17:57

140

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Dimension of boundary of a bounded domain; what to use for Sobolev inequalities

Published on 09 Jul 2016 - 15:06

62

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Show: If $u \in W^{1,p}(B_4(0))$ then $\int_{B_4(0)} \frac{|\nabla u|^p}{|x-a|^{n-1}} dx < \infty$ for a.e. $a \in B_1(0)$.

Published on 09 Jul 2016 - 22:21

50

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Bound of mollified in $H^{-2}$

Published on 26 Mar 2026 - 2:55

834

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Definition of the Laplacian as an operator from $H_0^1(\Omega)$ to $H_0^1(\Omega)'$

Published on 26 Mar 2026 - 12:15

66

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The convergence of $p$-laplace equation

Published on 26 Mar 2026 - 16:05

952

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Convergence of composition of functions in $L^p$

Published on 30 Mar 2026 - 16:45

212

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Do we have the same characterization of $(H^1(\Omega))^$ as that of $(H^1_0(\Omega))^$?

Published on 12 Jul 2016 - 5:09

30

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integral constraint induce a manifold on Sobolev space

Published on 25 Mar 2026 - 14:21

61

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Regularity of elliptic operators- no flux boundary conditions

Published on 27 Mar 2026 - 19:15

440

Views

Proof verification for the Friedrich's inequality in $\mathbb{R}$

Published on 13 Jul 2016 - 16:12

428

Views

Has the distributional Laplacian $\Delta f:C_c^\infty(\Omega)'\to C_c^\infty(\Omega)'$ a unique extension in $H_0^1(\Omega)'$?

Published on 26 Mar 2026 - 12:38

1.6k

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Relationship between the distributional Laplacian and the weak Laplacian

Published on 26 Mar 2026 - 12:35

506

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Conditions for membership of $H^2$

Published on 27 Mar 2026 - 19:15

100

Views

Closure of an operator

Published on 25 Mar 2026 - 14:39

List Question

Can we talk about the adjoint of a linear operator defined on a distribution space?

Dimension of boundary of a bounded domain; what to use for Sobolev inequalities

Show: If $u \in W^{1,p}(B_4(0))$ then $\int_{B_4(0)} \frac{|\nabla u|^p}{|x-a|^{n-1}} dx < \infty$ for a.e. $a \in B_1(0)$.

Bound of mollified in $H^{-2}$

Definition of the Laplacian as an operator from $H_0^1(\Omega)$ to $H_0^1(\Omega)'$

The convergence of $p$-laplace equation

Convergence of composition of functions in $L^p$

Do we have the same characterization of $(H^1(\Omega))^$ as that of $(H^1_0(\Omega))^$?

integral constraint induce a manifold on Sobolev space

Regularity of elliptic operators- no flux boundary conditions

Proof verification for the Friedrich's inequality in $\mathbb{R}$

Has the distributional Laplacian $\Delta f:C_c^\infty(\Omega)'\to C_c^\infty(\Omega)'$ a unique extension in $H_0^1(\Omega)'$?

Relationship between the distributional Laplacian and the weak Laplacian

Conditions for membership of $H^2$

Closure of an operator

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