Question

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

score 107 · Answer 1 · 2023-08-23 05:41:22

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

score 85 · Answer 2 · 2023-08-24 21:42:41

85

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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 24 Aug 2023 - 21:42

score 128 · Answer 3 · 2023-08-25 14:36:01

128

Views

Show that a nonlocal operator with symmetric kernel is well defined

Published on 25 Aug 2023 - 14:36

score 50 · Answer 4 · 2026-03-25 09:10:33

50

Views

What exactly is the "real interpolation space" $(L^q, W^{2,q})_{1-p^{-1},p}$ for $1<p,q<\infty$?

Published on 25 Mar 2026 - 9:10

score 112 · Answer 5 · 2023-08-29 03:56:20

112

Views

How to prove$|\cdot|^{s}g\in\mathcal{S}'$? a question from Bahouri-Chemin-Danchin book "fourier analysis and nonlinear pde"

Published on 29 Aug 2023 - 3:56

score 88 · Answer 6 · 2026-03-25 09:53:21

88

Views

Estimate the fractional Sobolev norm of Hermite functions.

Published on 25 Mar 2026 - 9:53

score 103 · Answer 7 · 2023-09-11 12:34:09

103

Views

maximum principle for compact manifolds

Published on 11 Sep 2023 - 12:34

score 68 · Answer 8 · 2023-09-14 08:36:15

68

Views

If $u\in D^{s, p}(\mathbb R^n)$, is that true that $u\in C(\mathbb R^n)$?

Published on 14 Sep 2023 - 8:36

score 33 · Answer 9 · 2023-09-17 14:20:04

33

Views

Relationship between Schwartz space and fractional Sobolev space

Published on 17 Sep 2023 - 14:20

score 51 · Answer 10 · 2023-09-21 07:37:19

51

Views

$H^{2}_{0}(\Omega)$ is embedded in $L^{\infty}(\Omega)$?

Published on 21 Sep 2023 - 7:37

score 44 · Answer 11 · 2023-09-21 11:57:50

44

Views

Is $H(div; \Omega ) \cap H(curl; \Omega )$ compactly embedd in $L^2(\Omega)$?

Published on 21 Sep 2023 - 11:57

score 386 · Answer 12 · 2023-09-25 11:55:50

386

Views

Fourier multipliers on $L^2(\mu)$

Published on 25 Sep 2023 - 11:55

score 39 · Answer 13 · 2023-10-14 22:13:06

39

Views

Norm on $H^1/2(\partial\Omega)$ by first isomorphism theorem.

Published on 14 Oct 2023 - 22:13

score 51 · Answer 14 · 2023-10-16 14:57:06

51

Views

equivalence of Sobolev space in manifolds

Published on 16 Oct 2023 - 14:57

score 98 · Answer 15 · 2023-10-16 22:19:30

98

Views

Dense subspace of radial functions of $H^1(\mathbb{R}^N)$

Published on 16 Oct 2023 - 22:19

List Question

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

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

Show that a nonlocal operator with symmetric kernel is well defined

What exactly is the "real interpolation space" $(L^q, W^{2,q})_{1-p^{-1},p}$ for $1<p,q<\infty$?

How to prove$|\cdot|^{s}g\in\mathcal{S}'$? a question from Bahouri-Chemin-Danchin book "fourier analysis and nonlinear pde"

Estimate the fractional Sobolev norm of Hermite functions.

maximum principle for compact manifolds

If $u\in D^{s, p}(\mathbb R^n)$, is that true that $u\in C(\mathbb R^n)$?

Relationship between Schwartz space and fractional Sobolev space

$H^{2}_{0}(\Omega)$ is embedded in $L^{\infty}(\Omega)$?

Is $H(div; \Omega ) \cap H(curl; \Omega )$ compactly embedd in $L^2(\Omega)$?

Fourier multipliers on $L^2(\mu)$

Norm on $H^1/2(\partial\Omega)$ by first isomorphism theorem.

equivalence of Sobolev space in manifolds

Dense subspace of radial functions of $H^1(\mathbb{R}^N)$

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