Question

If $t \to \lVert f(\cdot,t) \rVert_{L^2_x}^2$ is absolutely continuous, can we interchange the spatial integtal and time derivative?

score 81 · Answer 1 · 2026-02-23 19:23:25

81

Views

If $t \to \lVert f(\cdot,t) \rVert_{L^2_x}^2$ is absolutely continuous, can we interchange the spatial integtal and time derivative?

Published on 23 Feb 2026 - 19:23

score 65 · Answer 2 · 2026-03-27 00:57:02

65

Views

How do I find the weak derivative of this function?

Published on 27 Mar 2026 - 0:57

score 33 · Answer 3 · 2026-03-26 19:20:13

33

Views

Solution of PDE on Lipschitz domain which is in $\{ u \in H^1_0 : \Delta u \in L^2\}$ but not in $H^2$

Published on 26 Mar 2026 - 19:20

score 35 · Answer 4 · 2026-03-25 22:04:16

35

Views

Confusion with the definition of homogeneous Sobolev spaces

Published on 25 Mar 2026 - 22:04

score 95 · Answer 5 · 2026-03-25 20:11:00

95

Views

Brezis' exercise 8.17: is $D(A^*) \subset H^2 (I)$?

Published on 25 Mar 2026 - 20:11

score 56 · Answer 6 · 2026-03-25 11:03:27

56

Views

Is the Sobolev space $\dot{W}^{s,1}$ continuously embedded in the Besov space $\dot{B}^{s,1}_1$?

Published on 25 Mar 2026 - 11:03

score 54 · Answer 7 · 2023-11-17 18:47:25

54

Views

$\mathcal{H}^{-k}$ norm

Published on 17 Nov 2023 - 18:47

score 60 · Answer 8 · 2026-03-27 02:39:37

60

Views

Weak derivative of a function that is continuously differentiable except a finitely many points.

Published on 27 Mar 2026 - 2:39

score 47 · Answer 9 · 2023-11-20 14:22:16

47

Views

The range of weak gradient of a function in $W^{1,p}_{0}(\Omega)$

Published on 20 Nov 2023 - 14:22

score 61 · Answer 10 · 2023-11-20 16:11:16

61

Views

How to compare $L^p$ norm in the interior with the $L^p$ norm at the boundary?

Published on 20 Nov 2023 - 16:11

score 39 · Answer 11 · 2023-11-20 22:52:42

39

Views

Inlcusion of compactly supported Sobolev Space in Closure of $C_0^{\infty}\left(\mathbb{R}^n\right)$ in $W^{k,q}(\Omega)$

Published on 20 Nov 2023 - 22:52

score 68 · Answer 12 · 2026-04-02 11:15:14

68

Views

If $u$ is a distribution on the interval $(0, 1)$ such that $u' \in L^2 (I)$, then $u \in L^2 (I)$

Published on 02 Apr 2026 - 11:15

score 37 · Answer 13 · 2026-03-25 20:14:20

37

Views

Brezis' exercise 8.17: the domain of $A^*$ where $A u=u''-xu'$

Published on 25 Mar 2026 - 20:14

score 40 · Answer 14 · 2026-03-27 07:49:51

40

Views

Is the function $\int_0^{1} e^{-t H}e^{-2x^2}dt$ in $L^2$ with respect to the gaussian measure?

Published on 27 Mar 2026 - 7:49

score 97 · Answer 15 · 2026-03-30 18:11:09

97

Views

Dirac-Delta distribution lies in $H^{-1}(B_1(0))$ only for $n = 1$

Published on 30 Mar 2026 - 18:11

List Question

If $t \to \lVert f(\cdot,t) \rVert_{L^2_x}^2$ is absolutely continuous, can we interchange the spatial integtal and time derivative?

How do I find the weak derivative of this function?

Solution of PDE on Lipschitz domain which is in $\{ u \in H^1_0 : \Delta u \in L^2\}$ but not in $H^2$

Confusion with the definition of homogeneous Sobolev spaces

Brezis' exercise 8.17: is $D(A^*) \subset H^2 (I)$?

Is the Sobolev space $\dot{W}^{s,1}$ continuously embedded in the Besov space $\dot{B}^{s,1}_1$?

$\mathcal{H}^{-k}$ norm

Weak derivative of a function that is continuously differentiable except a finitely many points.

The range of weak gradient of a function in $W^{1,p}_{0}(\Omega)$

How to compare $L^p$ norm in the interior with the $L^p$ norm at the boundary?

Inlcusion of compactly supported Sobolev Space in Closure of $C_0^{\infty}\left(\mathbb{R}^n\right)$ in $W^{k,q}(\Omega)$

If $u$ is a distribution on the interval $(0, 1)$ such that $u' \in L^2 (I)$, then $u \in L^2 (I)$

Brezis' exercise 8.17: the domain of $A^*$ where $A u=u''-xu'$

Is the function $\int_0^{1} e^{-t H}e^{-2x^2}dt$ in $L^2$ with respect to the gaussian measure?

Dirac-Delta distribution lies in $H^{-1}(B_1(0))$ only for $n = 1$

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