List questions from sobolev-spaces

Published on 12 Apr 2026 - 17:51

128

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Is Sobolev limit of bijective maps surjective?

Published on 10 Apr 2026 - 23:13

241

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convergence of translation operators in Sobolev spaces

Published on 12 Apr 2026 - 6:24

54

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Proving that, if $\Vert f\Vert_{H^1}^2-\Vert g\Vert_{H^1}^2\to0$ and $\big\vert F(f)-F(g)\big\vert\to0$, then $\Vert f-g\Vert_{H^1}\to0$

Published on 16 Apr 2026 - 12:25

61

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Continuity in $H^\theta$ implies weak convergence in $H^s$

Published on 11 Apr 2026 - 0:50

76

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A type of Hölder function

Published on 13 Apr 2026 - 3:59

91

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If A is continuously embedded in B and $||u_{n}||_{A} \rightarrow +\infty$, can I say that $||u_{n}||_{B}\rightarrow +\infty?$

Published on 16 Apr 2026 - 11:45

245

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Scale Invariance of Sobolev Norms

Published on 09 Apr 2026 - 4:46

841

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Weak convergence in $H^1_0(\Omega)$ implies strong convergence in $L^{2^*}(\Omega)$.

Published on 13 Apr 2026 - 10:39

26

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Strong continuity of time-dependent functions with values in $H^s(\mathbb{R})$

Published on 07 Apr 2026 - 21:35

467

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Weak derivative and integral

Published on 12 Apr 2026 - 11:43

221

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Prove that a parabolic problem is well posed (Lax-Milgram lemma appilication)

Published on 15 Apr 2026 - 5:24

87

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Weak formuation $1-D$ advection diffusion equation: test function and solution in the same space $H_0^1$

Published on 13 Apr 2026 - 23:27

74

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How do I show that $u \in W^{k,1}(U)$ where $u(x)=|x|^{-\alpha}$?

Published on 12 Apr 2026 - 15:34

47

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Which space is $L^1(\partial\Omega)$?

Published on 01 Apr 2026 - 10:36

List Question

Weak partial derivative versus strong derivative

Is Sobolev limit of bijective maps surjective?

convergence of translation operators in Sobolev spaces

Proving that, if $\Vert f\Vert_{H^1}^2-\Vert g\Vert_{H^1}^2\to0$ and $\big\vert F(f)-F(g)\big\vert\to0$, then $\Vert f-g\Vert_{H^1}\to0$

Continuity in $H^\theta$ implies weak convergence in $H^s$

A type of Hölder function

If A is continuously embedded in B and $||u_{n}||_{A} \rightarrow +\infty$, can I say that $||u_{n}||_{B}\rightarrow +\infty?$

Scale Invariance of Sobolev Norms

Weak convergence in $H^1_0(\Omega)$ implies strong convergence in $L^{2^*}(\Omega)$.

Strong continuity of time-dependent functions with values in $H^s(\mathbb{R})$

Weak derivative and integral

Prove that a parabolic problem is well posed (Lax-Milgram lemma appilication)

Weak formuation $1-D$ advection diffusion equation: test function and solution in the same space $H_0^1$

How do I show that $u \in W^{k,1}(U)$ where $u(x)=|x|^{-\alpha}$?

Which space is $L^1(\partial\Omega)$?

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