List questions from sobolev-spaces

Published on 11 Apr 2026 - 12:30

138

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Reverse Poincaré inequality and Fourier Transform?

Published on 14 Apr 2026 - 3:12

65

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Find $a,b>0$ for which $||\langle x\rangle^{-b}|\partial_x|^{1/2}f||_{L^2}\lesssim||\partial_x f||_{L^2}+||\langle x\rangle^{-a}f||_{L^2}$

Published on 16 Apr 2026 - 17:22

88

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Clarification on the proof of Poincaré's inequality

Published on 10 Apr 2026 - 19:28

53

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Is this space reflexive Banach space?

Published on 14 Apr 2026 - 14:47

44

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Clarifications on the assumptions of Poincaré inequality

Published on 10 Apr 2026 - 17:13

54

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$L^s_\text{loc}(\Omega)$ with $\overline{\Omega}$ compact

Published on 15 Apr 2026 - 5:32

50

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On the support of a function given by an integral

Published on 12 Apr 2026 - 15:19

52

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Finding the norm of functional $f(u)=\int_0^{1/2} u(t)\,dt$ on Sobolev space $W^{2,1}[0,1]$.

Published on 14 Apr 2026 - 18:08

77

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Compute the distributional derivative of $1_{B(0,1)}$ on $\mathbb{R}^{2}$：$\partial_{j}1_{B(0,1)}$

Published on 19 Apr 2026 - 21:39

54

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Is there some connection between the Wronskian determinant and Sobolev spaces, e.g. $H^1$?

Published on 15 Apr 2026 - 4:42

56

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Weak derivative of Extension of a function in sobolev space

Published on 12 Apr 2026 - 4:35

175

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Compact support of $W^{1,p}_0$ functions

Published on 15 Apr 2026 - 20:32

38

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Notation for weak solutions in space and time

Published on 14 Apr 2026 - 4:15

25

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Isometry between $C^\infty_c$ and radially symmetric functions in the unit ball

Published on 15 Apr 2026 - 13:51

List Question

Determining what Sobolev space a function is in

Reverse Poincaré inequality and Fourier Transform?

Find $a,b>0$ for which $||\langle x\rangle^{-b}|\partial_x|^{1/2}f||_{L^2}\lesssim||\partial_x f||_{L^2}+||\langle x\rangle^{-a}f||_{L^2}$

Clarification on the proof of Poincaré's inequality

Is this space reflexive Banach space?

Clarifications on the assumptions of Poincaré inequality

$L^s_\text{loc}(\Omega)$ with $\overline{\Omega}$ compact

On the support of a function given by an integral

Finding the norm of functional $f(u)=\int_0^{1/2} u(t)\,dt$ on Sobolev space $W^{2,1}[0,1]$.

Compute the distributional derivative of $1_{B(0,1)}$ on $\mathbb{R}^{2}$：$\partial_{j}1_{B(0,1)}$

Is there some connection between the Wronskian determinant and Sobolev spaces, e.g. $H^1$?

Weak derivative of Extension of a function in sobolev space

Compact support of $W^{1,p}_0$ functions

Notation for weak solutions in space and time

Isometry between $C^\infty_c$ and radially symmetric functions in the unit ball

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