List questions from sobolev-spaces

Published on 17 Apr 2018 - 20:30

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Proof of Korn’s inequality

Published on 18 Apr 2018 - 7:54

833

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Norm of laplacian in dual space $H^{-2}$

Published on 22 Mar 2026 - 18:47

101

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H^s order of jump discontinuities

Published on 19 Mar 2026 - 16:57

297

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Coherence between Hamiltonian and Lagrangian in form of an inequality (Evans PDE)

Published on 23 Mar 2026 - 0:22

258

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Why $C_c^{\infty}(I)$ is not dense in $W^{1,p}(I)$

Published on 20 Apr 2018 - 1:01

303

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Sobolev Embedding Theorem

Published on 21 Apr 2018 - 3:09

87

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Step in the motivation of Lax-Milgram with membrane problem.

Published on 25 Mar 2026 - 23:37

208

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For $u$ in the Sobolev space $W^{k,p}(U)$, how to know $u$ or $D^\alpha u$ on the boundary of $U$?

Published on 25 Mar 2026 - 8:13

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Weak derivative of $|x|^\alpha$ in $\mathbb{R}^N \setminus \{0\}$

Published on 25 Mar 2026 - 8:09

420

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How to understand the derivative in sobolev space properly

Published on 23 Apr 2018 - 5:26

58

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If $(m-1)p\geq n$, $u(x)=|x|$ does not belong to $W^{m,p}(B(0,1))$.

Published on 23 Apr 2018 - 13:57

641

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Density argument in $H^2_0(\Omega)$.

Published on 23 Apr 2018 - 17:50

43

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What does $\limsup_{r \to 0} r^{-p}⨍_{B(x_0,r)} f^{q}(x) dx < \infty $ imply on the behavior of $f$?

Published on 24 Apr 2018 - 11:40

256

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Is $C^1(\Omega) \subseteq H^2(\Omega)$?

Published on 24 Mar 2026 - 20:47

List Question

Construction of a partition of unity on an open set $\Omega \subset \mathbb{R}^n$

Proof of Korn’s inequality

Norm of laplacian in dual space $H^{-2}$

H^s order of jump discontinuities

Coherence between Hamiltonian and Lagrangian in form of an inequality (Evans PDE)

Why $C_c^{\infty}(I)$ is not dense in $W^{1,p}(I)$

Sobolev Embedding Theorem

Step in the motivation of Lax-Milgram with membrane problem.

For $u$ in the Sobolev space $W^{k,p}(U)$, how to know $u$ or $D^\alpha u$ on the boundary of $U$?

Weak derivative of $|x|^\alpha$ in $\mathbb{R}^N \setminus \{0\}$

How to understand the derivative in sobolev space properly

If $(m-1)p\geq n$, $u(x)=|x|$ does not belong to $W^{m,p}(B(0,1))$.

Density argument in $H^2_0(\Omega)$.

What does $\limsup_{r \to 0} r^{-p}⨍_{B(x_0,r)} f^{q}(x) dx < \infty $ imply on the behavior of $f$?

Is $C^1(\Omega) \subseteq H^2(\Omega)$?

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