List questions from sobolev-spaces

Published on 02 Apr 2026 - 2:29

37

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Bounded sequence in $W^{1,1}(\Omega)$ in 1D

Published on 20 Aug 2023 - 8:58

182

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Morrey's inequality proof, Evans PDE.

Published on 20 Aug 2023 - 9:43

23

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For $f \in H^1(\mathbb{T}^n)$ and some open $A \subset \mathbb{T}^n$, which space does $f \cdot \chi_{A}$ belong to?

Published on 21 Aug 2023 - 9:34

37

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Are functions in $W^{1,p}(\Omega)$ bounded when $p> N$?

Published on 21 Aug 2023 - 15:36

62

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Inequality involving the Gagliardo seminorm

Published on 25 Mar 2026 - 12:53

108

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How do I show that the definition of Sobolev–Slobodeckij spaces $W^{s,p}(\Omega)$ coincides with the classical one when $s$ is integer.

Published on 25 Mar 2026 - 22:05

91

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Proof of the Sobolev Extension Theorem in Evans' PDE

Published on 24 Aug 2023 - 9:15

83

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Compact Embedding/ Sobolev's Theorem

Published on 28 Mar 2026 - 8:47

170

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Weak convergence in Sobolev space $W^{1,p}$ implies strong convergence in $L^p$

Published on 24 Aug 2023 - 20:26

86

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The integral $\int_{\mathbb{R}^N} \int_{|x - y| \geq 1} \dfrac{|u(x)|^p}{|x - y|^{N+sp}}dxdy$ is finite?

Published on 25 Mar 2026 - 19:07

67

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Existence of a solution to the Dirichlet problem

Published on 30 Mar 2026 - 7:54

97

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Divergence theorem in Sobolev spaces

Published on 25 Mar 2026 - 6:18

65

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Composition of $H^2$ functions

Published on 28 Mar 2026 - 5:01

39

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Existence of a weak solution to the Poisson equation for $p \neq 2$

Published on 27 Aug 2023 - 10:48

List Question

Why characteristic functions of regular domains are not in $W^{1,p}$?

Bounded sequence in $W^{1,1}(\Omega)$ in 1D

Morrey's inequality proof, Evans PDE.

For $f \in H^1(\mathbb{T}^n)$ and some open $A \subset \mathbb{T}^n$, which space does $f \cdot \chi_{A}$ belong to?

Are functions in $W^{1,p}(\Omega)$ bounded when $p> N$?

Inequality involving the Gagliardo seminorm

How do I show that the definition of Sobolev–Slobodeckij spaces $W^{s,p}(\Omega)$ coincides with the classical one when $s$ is integer.

Proof of the Sobolev Extension Theorem in Evans' PDE

Compact Embedding/ Sobolev's Theorem

Weak convergence in Sobolev space $W^{1,p}$ implies strong convergence in $L^p$

The integral $\int_{\mathbb{R}^N} \int_{|x - y| \geq 1} \dfrac{|u(x)|^p}{|x - y|^{N+sp}}dxdy$ is finite?

Existence of a solution to the Dirichlet problem

Divergence theorem in Sobolev spaces

Composition of $H^2$ functions

Existence of a weak solution to the Poisson equation for $p \neq 2$

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