Question

Defining a fractional derivative operator over Laplace transforms

score 144 · Answer 1 · 2023-07-15 23:25:54

144

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Defining a fractional derivative operator over Laplace transforms

Published on 15 Jul 2023 - 23:25

score 63 · Answer 2 · 2023-07-30 02:54:04

63

Views

Equivalence norm in $W^{s, p}(\mathbb{R}^n)$ and Gagliardo seminorm $[u]_{s, p}$

Published on 30 Jul 2023 - 2:54

score 94 · Answer 3 · 2026-03-25 09:26:14

94

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Are there a solutions for $\frac{\mathrm{d}^\alpha f}{\mathrm{d}x^\alpha} = xe^x$?

Published on 25 Mar 2026 - 9:26

score 36 · Answer 4 · 2023-08-20 22:39:52

36

Views

Understanding some calculations about the kernel of the fractional laplace operator

Published on 20 Aug 2023 - 22:39

score 102 · Answer 5 · 2023-08-28 04:07:59

102

Views

Show that $G_t(x)=(2\pi)^{-n/2}\int_{\mathbb{R}^n}\mathbb{e}^{ix\cdot\xi}\mathrm{e}^{-t(1+|\xi|^2)^{\alpha}}\,d\xi$ is uniformly bounded in $L^1$.

Published on 28 Aug 2023 - 4:07

score 29 · Answer 6 · 2023-09-12 03:16:41

29

Views

If $\widetilde{u}(x) = u(-x)$, what is $[\widetilde u]^2_s$?

Published on 12 Sep 2023 - 3:16

score 69 · Answer 7 · 2026-03-25 19:06:00

69

Views

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

Published on 25 Mar 2026 - 19:06

score 22 · Answer 8 · 2026-03-24 23:43:53

22

Views

Functional Application of the Differential Operator: Can the Order of Differentiation be a Function?

Published on 24 Mar 2026 - 23:43

score 55 · Answer 9 · 2023-09-24 10:32:25

55

Views

How to prove that $\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\in L^1(\mathbb R^{2n})$?

Published on 24 Sep 2023 - 10:32

score 62 · Answer 10 · 2023-09-25 11:41:45

62

Views

Convolution and fractional operator

Published on 25 Sep 2023 - 11:41

score 18 · Answer 11 · 2023-09-27 08:15:18

18

Views

Fractional differintegral for the reconstruction of time series

Published on 27 Sep 2023 - 8:15

score 99 · Answer 12 · 2026-03-25 18:53:43

99

Views

What is the relationship between Hölder spaces and differentiability?

Published on 25 Mar 2026 - 18:53

score 77 · Answer 13 · 2023-10-06 23:51:44

77

Views

Does $u$ solve $(-\Delta)^s u =0$ in $(-r, r)$ and $u=g$ in $\mathbb R\setminus (-r, r)$?

Published on 06 Oct 2023 - 23:51

score 51 · Answer 14 · 2023-10-07 03:50:04

51

Views

Does Green's formula for the ball contain the Poisson's kernel?

Published on 07 Oct 2023 - 3:50

score 26 · Answer 15 · 2023-10-20 13:51:55

26

Views

What do I need to know for deriving the limits of sequences of discrete convolutions?

Published on 20 Oct 2023 - 13:51

List Question

Defining a fractional derivative operator over Laplace transforms

Equivalence norm in $W^{s, p}(\mathbb{R}^n)$ and Gagliardo seminorm $[u]_{s, p}$

Are there a solutions for $\frac{\mathrm{d}^\alpha f}{\mathrm{d}x^\alpha} = xe^x$?

Understanding some calculations about the kernel of the fractional laplace operator

Show that $G_t(x)=(2\pi)^{-n/2}\int_{\mathbb{R}^n}\mathbb{e}^{ix\cdot\xi}\mathrm{e}^{-t(1+|\xi|^2)^{\alpha}}\,d\xi$ is uniformly bounded in $L^1$.

If $\widetilde{u}(x) = u(-x)$, what is $[\widetilde u]^2_s$?

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

Functional Application of the Differential Operator: Can the Order of Differentiation be a Function?

How to prove that $\frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}\in L^1(\mathbb R^{2n})$?

Convolution and fractional operator

Fractional differintegral for the reconstruction of time series

What is the relationship between Hölder spaces and differentiability?

Does $u$ solve $(-\Delta)^s u =0$ in $(-r, r)$ and $u=g$ in $\mathbb R\setminus (-r, r)$?

Does Green's formula for the ball contain the Poisson's kernel?

What do I need to know for deriving the limits of sequences of discrete convolutions?

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