List questions from sobolev-spaces

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$f\in C([0,T];C^1(\Omega))$ implies $f \in C([0,T];W^{1,p}(\Omega))$?

Published on 17 Apr 2026 - 2:51

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If a sequence of smooth functions converge in the Sobolev norm, what can one say about the limiting function?

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Extending $W^{2,n}(\Omega)\cap C^2(\Omega)$-functions to $W^{2,n}(\Omega)$

Published on 14 Apr 2026 - 14:30

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Trace spaces of Orlicz-Sobolev spaces.

Published on 10 Apr 2026 - 22:17

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What can be said about the eigenvalues of the Laplace operator in $H^k(\mathbb{T}^2)$

Published on 12 Apr 2026 - 2:42

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How to show that $\int_0^T (u_m(t), u_m(t))_{H} \to \int_0^T (u(t), u(t))?$ (Bochner space)

Published on 15 Apr 2026 - 21:00

204

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Continuous and dense embeddings and the density of sets in Hilbert space.

Published on 13 Apr 2026 - 2:43

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Existence of weak solution in Sobolev space $W^{1,p}$

Published on 16 Apr 2026 - 14:17

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An inequality of J. Necas

Published on 09 Apr 2026 - 11:56

62

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A projection error estimation in Sobolev space of Fractional order (1D)

Published on 12 Apr 2026 - 12:26

415

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Blow up of solutions to parabolic PDE

Published on 17 Apr 2026 - 2:33

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Can you explain to me this property! True or false?

Published on 15 Apr 2026 - 0:38

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Is $W_0^{1,p}(\Omega)$ complemented in $W^{1,p}(\Omega)$?

Published on 16 Apr 2026 - 7:48

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Extension of Sobolev functions

Published on 11 Apr 2026 - 12:49

List Question

$H^2$ and $C^1$ - Sobolev space

$f\in C([0,T];C^1(\Omega))$ implies $f \in C([0,T];W^{1,p}(\Omega))$?

If a sequence of smooth functions converge in the Sobolev norm, what can one say about the limiting function?

Extending $W^{2,n}(\Omega)\cap C^2(\Omega)$-functions to $W^{2,n}(\Omega)$

Trace spaces of Orlicz-Sobolev spaces.

What can be said about the eigenvalues of the Laplace operator in $H^k(\mathbb{T}^2)$

How to show that $\int_0^T (u_m(t), u_m(t))_{H} \to \int_0^T (u(t), u(t))?$ (Bochner space)

Continuous and dense embeddings and the density of sets in Hilbert space.

Existence of weak solution in Sobolev space $W^{1,p}$

An inequality of J. Necas

A projection error estimation in Sobolev space of Fractional order (1D)

Blow up of solutions to parabolic PDE

Can you explain to me this property! True or false?

Is $W_0^{1,p}(\Omega)$ complemented in $W^{1,p}(\Omega)$?

Extension of Sobolev functions

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