List questions from sobolev-spaces

Published on 07 Apr 2026 - 21:06

91

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Is there a standard terminology for $|f^{-1}(y)|=1$ for almost every $y$?

Published on 15 Apr 2026 - 14:10

108

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Convergence in $L^{\infty}$ implies convergence in $W^{1,p}((0,1))$

Published on 15 Apr 2026 - 2:41

46

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Sobolev embeddings lowering the order of integrability

Published on 13 Apr 2026 - 8:46

71

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How the Sobolev embedding used in this case

Published on 12 Apr 2026 - 8:17

76

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Norm characterization on Sobolev Spaces $W^{k,p}(\mathbb{R}^n)$.

Published on 14 Apr 2026 - 4:14

130

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Problems on Sobolev space $H_0^1$

Published on 12 Apr 2026 - 12:24

95

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Non trivial Eigenvectors of the Laplacian in $H^1$

Published on 15 Apr 2026 - 1:06

74

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How to get $2\langle \nabla u, \partial_t \nabla u \rangle=\frac{d}{dt}\|\nabla u\|^2_{L^2(U)}$

Published on 17 Apr 2026 - 5:55

63

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reference for Poincaré constant of $W_0^{1,1}(B)$

Published on 16 Apr 2026 - 5:00

38

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Second order partial derivatives of Sobolev functions.

Published on 13 Apr 2026 - 22:43

341

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Characterizing Sobolev spaces using Fourier transformation

Published on 12 Apr 2026 - 9:41

39

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$L^{P} ( \Omega ; W^{1,P}(Y))$ can someone define this space. $L^{P}$ and $W^{1,P}$ are sobolve and Lp spaces. How norm can define?

Published on 16 Apr 2026 - 9:18

175

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Multiplication by a smooth compactly supported function in homogeneous Sobolev spaces

Published on 13 Apr 2026 - 23:48

135

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How does Sobolev norm change with respect to domain size?

Published on 09 Apr 2026 - 14:45

List Question

Function in $L^2(\Omega)$ is in $H^1(\Omega)$

Is there a standard terminology for $|f^{-1}(y)|=1$ for almost every $y$?

Convergence in $L^{\infty}$ implies convergence in $W^{1,p}((0,1))$

Sobolev embeddings lowering the order of integrability

How the Sobolev embedding used in this case

Norm characterization on Sobolev Spaces $W^{k,p}(\mathbb{R}^n)$.

Problems on Sobolev space $H_0^1$

Non trivial Eigenvectors of the Laplacian in $H^1$

How to get $2\langle \nabla u, \partial_t \nabla u \rangle=\frac{d}{dt}\|\nabla u\|^2_{L^2(U)}$

reference for Poincaré constant of $W_0^{1,1}(B)$

Second order partial derivatives of Sobolev functions.

Characterizing Sobolev spaces using Fourier transformation

$L^{P} ( \Omega ; W^{1,P}(Y))$ can someone define this space. $L^{P}$ and $W^{1,P}$ are sobolve and Lp spaces. How norm can define?

Multiplication by a smooth compactly supported function in homogeneous Sobolev spaces

How does Sobolev norm change with respect to domain size?

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