List questions from fractional-sobolev-spaces

Published on 20 May 2023 - 10:41

74

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Integral representation for the operator $\frac{\log{\Delta}}{\Delta}$ in two dimensions

Published on 22 Mar 2026 - 10:00

163

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Does the equality $\|\nabla u\|^{p}_{L^{p}(\mathbb{R}^{n})}=[u]^{p}_{W^{s,p}(\Omega)}$ hold in the fractional Sobolev space?

Published on 24 May 2023 - 4:12

187

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Show that the fractional Laplacian operator is closed

Published on 01 Jun 2023 - 15:17

35

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Associating a non-local differential operator to its integral representation

Published on 21 Mar 2026 - 23:40

45

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A continuous function in $W^{1,p}(I)$ function with continuous weak derivative is a $C^1(\overline{I})$ function

Published on 16 Jun 2023 - 13:10

56

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Using Semigroup Theory of Linear Operators to show that the operator $(-\Delta)^s$ is closed.

Published on 25 Mar 2026 - 7:44

24

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Embedding in compact manifold

Published on 18 Jun 2023 - 6:48

107

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Proving the existence of a solution of the fractional heat equation using semigroup methods

Published on 18 Jun 2023 - 20:21

42

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Functional convergence in $W^{s,p}(M)$

Published on 20 Jun 2023 - 13:36

38

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Multiplication in fractional sobolev spaces

Published on 20 Jun 2023 - 23:50

149

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Dirichlet and Neumann Traces in $H^{2}(\Omega)$, $\Omega$ Lipschitz and Unbounded

Published on 29 Jun 2023 - 15:08

35

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Proving that a $W^{1,2}$ type space is Hilbert

Published on 21 Jul 2023 - 17:38

41

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Weak convergence in $W^{2, p}_{loc}(R^{N})$

Published on 21 Jul 2023 - 23:45

61

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Inequality involving the Gagliardo seminorm

Published on 22 Aug 2023 - 17:07

List Question

Weak equality equation with a negative fractional Sobolev space.

Integral representation for the operator $\frac{\log{\Delta}}{\Delta}$ in two dimensions

Does the equality $\|\nabla u\|^{p}_{L^{p}(\mathbb{R}^{n})}=[u]^{p}_{W^{s,p}(\Omega)}$ hold in the fractional Sobolev space?

Show that the fractional Laplacian operator is closed

Associating a non-local differential operator to its integral representation

A continuous function in $W^{1,p}(I)$ function with continuous weak derivative is a $C^1(\overline{I})$ function

Using Semigroup Theory of Linear Operators to show that the operator $(-\Delta)^s$ is closed.

Embedding in compact manifold

Proving the existence of a solution of the fractional heat equation using semigroup methods

Functional convergence in $W^{s,p}(M)$

Multiplication in fractional sobolev spaces

Dirichlet and Neumann Traces in $H^{2}(\Omega)$, $\Omega$ Lipschitz and Unbounded

Proving that a $W^{1,2}$ type space is Hilbert

Weak convergence in $W^{2, p}_{loc}(R^{N})$

Inequality involving the Gagliardo seminorm

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