Question

Convolution of Mollifier and function $f$ converges to $f$ on all compact subsets?

score 48 · Answer 1 · 2023-11-28 19:21:50

48

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Convolution of Mollifier and function $f$ converges to $f$ on all compact subsets?

Published on 28 Nov 2023 - 19:21

score 57 · Answer 2 · 2023-12-10 22:26:42

57

Views

On partial integration of $W^{1,p}_0(U)$ functions and boundary terms.

Published on 10 Dec 2023 - 22:26

score 81 · Answer 3 · 2023-12-11 18:06:50

81

Views

$u, v \in H^1(\Omega)$, then the product $uv \in W^{1,3/2}(\Omega)$ for $\Omega \subset \mathbb{R}^3$?

Published on 11 Dec 2023 - 18:06

score 29 · Answer 4 · 2026-03-25 07:54:21

29

Views

Is there a way to prove the theorem of Trace as in Evans, in the picture below, using only weak derivatives?

Published on 25 Mar 2026 - 7:54

score 31 · Answer 5 · 2026-02-23 19:24:01

31

Views

Convergence of the derivatives implies convergence of the original functions on $1$-dimension.

Published on 23 Feb 2026 - 19:24

score 30 · Answer 6 · 2026-03-26 21:12:28

30

Views

A function with weak derivatives in two dimension also has weak derivative in one dimension?

Published on 26 Mar 2026 - 21:12

score 30 · Answer 7 · 2023-12-27 09:53:47

30

Views

Calculate the weak derivative of a dual product

Published on 27 Dec 2023 - 9:53

score 34 · Answer 8 · 2023-12-29 00:41:55

34

Views

Almost everywhere differentiability implies weak differentiability on the real line, without additional assumption of any integrability?

Published on 29 Dec 2023 - 0:41

score 25 · Answer 9 · 2023-12-29 01:09:09

25

Views

$\mathscr{F} (\partial_{\alpha} \varphi)=i^{|\alpha|} x^\alpha \mathscr{F}\varphi$ on $H_0^m$ valid?

Published on 29 Dec 2023 - 1:09

score 59 · Answer 10 · 2024-01-04 11:19:20

59

Views

A basic question about $H^1(\Omega)$ Sobolev space

Published on 04 Jan 2024 - 11:19

score 41 · Answer 11 · 2024-01-06 11:20:21

41

Views

weak $\alpha$ derivative of the moltification of a function

Published on 06 Jan 2024 - 11:20

score 33 · Answer 12 · 2024-01-07 21:31:43

33

Views

Checking coercivity

Published on 07 Jan 2024 - 21:31

score 61 · Answer 13 · 2024-01-16 11:28:09

61

Views

Proving that the absolute value function does not have second weak derivative

Published on 16 Jan 2024 - 11:28

score 52 · Answer 14 · 2024-01-17 06:41:56

52

Views

Weak solution of PDE

Published on 17 Jan 2024 - 6:41

score 33 · Answer 15 · 2026-03-26 00:59:57

33

Views

$\Delta (u^m)=\mathrm{div}(m u^{m-1} \mathrm{grad}(u))$?

Published on 26 Mar 2026 - 0:59

List Question

Convolution of Mollifier and function $f$ converges to $f$ on all compact subsets?

On partial integration of $W^{1,p}_0(U)$ functions and boundary terms.

$u, v \in H^1(\Omega)$, then the product $uv \in W^{1,3/2}(\Omega)$ for $\Omega \subset \mathbb{R}^3$?

Is there a way to prove the theorem of Trace as in Evans, in the picture below, using only weak derivatives?

Convergence of the derivatives implies convergence of the original functions on $1$-dimension.

A function with weak derivatives in two dimension also has weak derivative in one dimension?

Calculate the weak derivative of a dual product

Almost everywhere differentiability implies weak differentiability on the real line, without additional assumption of any integrability?

$\mathscr{F} (\partial_{\alpha} \varphi)=i^{|\alpha|} x^\alpha \mathscr{F}\varphi$ on $H_0^m$ valid?

A basic question about $H^1(\Omega)$ Sobolev space

weak $\alpha$ derivative of the moltification of a function

Checking coercivity

Proving that the absolute value function does not have second weak derivative

Weak solution of PDE

$\Delta (u^m)=\mathrm{div}(m u^{m-1} \mathrm{grad}(u))$?

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