List questions from sobolev-spaces

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Analytical solution to Laplace equation for comparison with FEM solution

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176

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second- order parabolic PDE as semigroups ( Evans 7.4.2)

Published on 16 Apr 2026 - 16:23

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Proving $(1+|\xi|^2)^{-s/2}\widehat{u} \in L^2(\mathbb{R}^n)$

Published on 17 Apr 2026 - 4:33

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How to prove $u\in W^{1,p}_0(\Omega^+)$?

Published on 13 Apr 2026 - 19:52

85

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$L^1$ cannot be embedded into Sobolev $H^{-\frac{n}{2}}(\mathbb{R^n})$

Published on 13 Apr 2026 - 1:26

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Compactness of the inverse Laplacian.

Published on 14 Apr 2026 - 18:06

184

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$H_0^1(\mathbb{R}^d \setminus \{0\}) = H^1(\mathbb{R}^d \setminus \{0\})$ for $d = 2$

Published on 16 Apr 2026 - 23:03

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The logic about the derivation for variational formulation

Published on 12 Apr 2026 - 8:03

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Is $H^{\frac{1}{2}}(\partial \Omega)\times H^{-\frac{1}{2}}(\partial \Omega)$ a Hilbert space?

Published on 13 Apr 2026 - 16:00

84

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Prove that a clasical solution exists and is unique for the boundary value problem

Published on 16 Apr 2026 - 2:39

88

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Continuity and $L^p$ norm

Published on 13 Apr 2026 - 19:31

358

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Why the normal trace operator for H(div;) is surjective? I think proof is wrong..

Published on 14 Apr 2026 - 2:57

138

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How to prove that a strong solution of the homogeneous Dirichlet boundary problem really exists?

Published on 11 Apr 2026 - 4:07

106

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Trace property of $H_0^1(\Omega)$

Published on 11 May 2026 - 2:15

List Question

Extension of a zero functional from $H_0^1(\Omega)$ to $H^1(\Omega)$

Analytical solution to Laplace equation for comparison with FEM solution

second- order parabolic PDE as semigroups ( Evans 7.4.2)

Proving $(1+|\xi|^2)^{-s/2}\widehat{u} \in L^2(\mathbb{R}^n)$

How to prove $u\in W^{1,p}_0(\Omega^+)$?

$L^1$ cannot be embedded into Sobolev $H^{-\frac{n}{2}}(\mathbb{R^n})$

Compactness of the inverse Laplacian.

$H_0^1(\mathbb{R}^d \setminus \{0\}) = H^1(\mathbb{R}^d \setminus \{0\})$ for $d = 2$

The logic about the derivation for variational formulation

Is $H^{\frac{1}{2}}(\partial \Omega)\times H^{-\frac{1}{2}}(\partial \Omega)$ a Hilbert space?

Prove that a clasical solution exists and is unique for the boundary value problem

Continuity and $L^p$ norm

Why the normal trace operator for H(div;) is surjective? I think proof is wrong..

How to prove that a strong solution of the homogeneous Dirichlet boundary problem really exists?

Trace property of $H_0^1(\Omega)$

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