List questions from fractional-sobolev-spaces

20

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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 15 Apr 2026 - 22:44

37

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Confusion with the definition of homogeneous Sobolev spaces

Published on 10 Apr 2026 - 21:10

34

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Compactness criterion on subsets of fractional Sobolev spaces

Published on 14 Apr 2026 - 19:26

86

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

Published on 13 Apr 2026 - 0:31

36

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Compactness criterion for subsets in a fractional sobolev space

Published on 09 Apr 2026 - 19:45

100

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

Published on 14 Apr 2026 - 20:25

100

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

Published on 13 Apr 2026 - 2:09

46

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Questions on Sobolev Spaces and the Laplacian Operator

Published on 09 Apr 2026 - 20:06

34

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

Published on 15 Apr 2026 - 22:49

32

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

Published on 12 Apr 2026 - 8:59

84

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Proving that a weighted Sobolev space is a Hilbert space

Published on 13 Apr 2026 - 7:16

59

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

Published on 10 May 2026 - 21:59

72

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

Published on 15 Apr 2026 - 0:17

53

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

Published on 12 Apr 2026 - 19:53

30

Views

Question on the definition of fractional sobolev norm

Published on 11 Apr 2026 - 0:04

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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