List questions from sobolev-spaces

Published on 08 Apr 2026 - 18:37

71

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Interpolated Sobolev norm inequality

Published on 09 Apr 2026 - 3:40

139

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Frechet differentiability of superposition operators $F\colon H^1(\Omega) \to L^2(\Omega)$

Published on 12 Apr 2026 - 19:36

519

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$W^{1,p}(\Omega) \hookrightarrow L^p(\Omega)$

Published on 14 Apr 2026 - 21:09

215

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"Doubly Lipschitz" functions

Published on 14 Apr 2026 - 14:19

468

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Norm in a Sobolev Space

Published on 11 Apr 2026 - 16:43

23

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Can we find a $W_{0}^{1,\infty}$ solution of some given partial differential equations?

Published on 24 Apr 2026 - 1:46

116

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Sobolev regularity of the distributional derivatives

Published on 12 Apr 2026 - 17:19

100

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Extension of Sobolev function in 1D

Published on 12 Apr 2026 - 5:28

46

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Is there some function in $C^1(U)$ but not $W^{1,p}(U)$

Published on 16 Apr 2026 - 6:22

87

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If $\varphi \in C^\infty_0(\Omega)$ and $u \in H^1(\Omega)$ then $\varphi u \in W^{1, 2}_0(\Omega)$?

Published on 14 Apr 2026 - 5:14

37

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An inequality for the $W^{k,1}(\mathbb{R}^n)$

Published on 10 Apr 2026 - 12:03

88

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Prove $H^k(\mathbb{R}^n) = W^{k,2}(\mathbb{R}^n)$

Published on 14 Apr 2026 - 4:37

333

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Two equivalent norms on a Sobolev space

Published on 15 Apr 2026 - 23:30

143

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PDE Theory and Sobolev Spaces

Published on 11 Apr 2026 - 6:58

List Question

Integrability of pointwise global Lipschitz constant

Interpolated Sobolev norm inequality

Frechet differentiability of superposition operators $F\colon H^1(\Omega) \to L^2(\Omega)$

$W^{1,p}(\Omega) \hookrightarrow L^p(\Omega)$

"Doubly Lipschitz" functions

Norm in a Sobolev Space

Can we find a $W_{0}^{1,\infty}$ solution of some given partial differential equations?

Sobolev regularity of the distributional derivatives

Extension of Sobolev function in 1D

Is there some function in $C^1(U)$ but not $W^{1,p}(U)$

If $\varphi \in C^\infty_0(\Omega)$ and $u \in H^1(\Omega)$ then $\varphi u \in W^{1, 2}_0(\Omega)$?

An inequality for the $W^{k,1}(\mathbb{R}^n)$

Prove $H^k(\mathbb{R}^n) = W^{k,2}(\mathbb{R}^n)$

Two equivalent norms on a Sobolev space

PDE Theory and Sobolev Spaces

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