List questions from sobolev-spaces

Published on 12 Apr 2026 - 3:21

97

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$\Delta u = f $ in $ \Omega = (0,1)^2, u=0$ in $\partial \Omega$ Prove $ |u|_{H^2(\Omega)} =||\Delta u||_{L^2(\Omega)}$

Published on 11 Apr 2026 - 0:58

123

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Extend a $C^2$ function from the Boundary to the Interior while Preserving Some Regularity

Published on 16 Apr 2026 - 4:21

154

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$W^{k,p}_{0}$ is scale invariant

Published on 11 Apr 2026 - 13:55

228

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Poincare inequality in Sobolev space without zero boundary value

Published on 12 Apr 2026 - 3:59

77

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Prove something is in $L^2(\mathbb{R}^+)$

Published on 14 Apr 2026 - 4:38

267

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A compact embedding for sobolev space H^{1} (to holder space ?)

Published on 09 Apr 2026 - 3:37

195

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Poincare Inequality for Mean-Zero Functions

Published on 09 Apr 2026 - 16:05

64

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How to prove that this sequence has a convergent subsequence in some $L^p(\Omega)$

Published on 11 Apr 2026 - 23:54

94

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Can the weak derivative be more regular than the function itself?

Published on 12 Apr 2026 - 12:03

70

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continuous linear operator (isomorphism) on $H^1$

Published on 09 Apr 2026 - 8:48

225

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How does the trace operator resolve the "restriction to the boundary" issue in Sobolev spaces?

Published on 08 Apr 2026 - 16:46

128

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Two function equal a.e then their weak derivative is the same ? Sobolev

Published on 08 Apr 2026 - 20:14

154

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Variational characterisation of Neumann eigenvalue

Published on 12 Apr 2026 - 15:18

30

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extension for convex sets in $W^{1,p}$ spaces

Published on 16 Apr 2026 - 12:57

List Question

is $H^2\subset L^{\infty}$

$\Delta u = f $ in $ \Omega = (0,1)^2, u=0$ in $\partial \Omega$ Prove $ |u|_{H^2(\Omega)} =||\Delta u||_{L^2(\Omega)}$

Extend a $C^2$ function from the Boundary to the Interior while Preserving Some Regularity

$W^{k,p}_{0}$ is scale invariant

Poincare inequality in Sobolev space without zero boundary value

Prove something is in $L^2(\mathbb{R}^+)$

A compact embedding for sobolev space H^{1} (to holder space ?)

Poincare Inequality for Mean-Zero Functions

How to prove that this sequence has a convergent subsequence in some $L^p(\Omega)$

Can the weak derivative be more regular than the function itself?

continuous linear operator (isomorphism) on $H^1$

How does the trace operator resolve the "restriction to the boundary" issue in Sobolev spaces?

Two function equal a.e then their weak derivative is the same ? Sobolev

Variational characterisation of Neumann eigenvalue

extension for convex sets in $W^{1,p}$ spaces

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