List questions from fractional-sobolev-spaces

18

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Compact embedding of $D^{s,p}(\mathbb{R}^N)$ into $L_{loc}^{r}(\mathbb{R}^N)$ for every $r \in [1,p_{s}^)$, where $p_{s}^{}=\frac{Np}{N-sp}, sp<N$

Published on 20 Mar 2026 - 0:53

34

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Confusion with the definition of homogeneous Sobolev spaces

Published on 13 Nov 2023 - 20:36

31

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Compactness criterion on subsets of fractional Sobolev spaces

Published on 28 Nov 2023 - 12:01

83

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Is $H^s(\mathbb R^n)$ continuously embedded in $L^2(\mathbb R^n)$ when $2s>n$?

Published on 28 Nov 2023 - 13:35

33

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Compactness criterion for subsets in a fractional sobolev space

Published on 29 Nov 2023 - 19:42

97

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The space $H^s(\mathbb R)$ and the embedding in $L^p_{loc}(\mathbb R)$: for which $p$?

Published on 02 Dec 2023 - 9:00

97

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Pre-compactness of $H^s(\mathbb R)$ when $s\in (\frac12, 1)$

Published on 05 Dec 2023 - 11:45

43

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Questions on Sobolev Spaces and the Laplacian Operator

Published on 06 Dec 2023 - 13:59

31

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$L^2(G)$ convergence $\Rightarrow$ $H_0^s(G)$ convergence?

Published on 09 Dec 2023 - 22:24

29

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Functions in $H_0^s(U)$ disappear on their boundaries?

Published on 10 Dec 2023 - 20:30

81

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Proving that a weighted Sobolev space is a Hilbert space

Published on 11 Dec 2023 - 23:02

58

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Connection between $H^s_0(\Omega)$ defined by Fourriertransform and $H^s_0(\Omega)$ defined canonically.

Published on 25 Mar 2026 - 12:54

69

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Equivalent norms on $H^s$ $s>1$

Published on 30 Dec 2023 - 1:58

50

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Definition of $H_0^s(\Omega)$ via Fourier transform

Published on 01 Jan 2024 - 22:21

27

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Question on the definition of fractional sobolev norm

Published on 07 Jan 2024 - 14:18

List Question

Compact embedding of $D^{s,p}(\mathbb{R}^N)$ into $L_{loc}^{r}(\mathbb{R}^N)$ for every $r \in [1,p_{s}^)$, where $p_{s}^{}=\frac{Np}{N-sp}, sp<N$

Confusion with the definition of homogeneous Sobolev spaces

Compactness criterion on subsets of fractional Sobolev spaces

Is $H^s(\mathbb R^n)$ continuously embedded in $L^2(\mathbb R^n)$ when $2s>n$?

Compactness criterion for subsets in a fractional sobolev space

The space $H^s(\mathbb R)$ and the embedding in $L^p_{loc}(\mathbb R)$: for which $p$?

Pre-compactness of $H^s(\mathbb R)$ when $s\in (\frac12, 1)$

Questions on Sobolev Spaces and the Laplacian Operator

$L^2(G)$ convergence $\Rightarrow$ $H_0^s(G)$ convergence?

Functions in $H_0^s(U)$ disappear on their boundaries?

Proving that a weighted Sobolev space is a Hilbert space

Connection between $H^s_0(\Omega)$ defined by Fourriertransform and $H^s_0(\Omega)$ defined canonically.

Equivalent norms on $H^s$ $s>1$

Definition of $H_0^s(\Omega)$ via Fourier transform

Question on the definition of fractional sobolev norm

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