List questions from sobolev-spaces

Published on 16 Apr 2026 - 20:46

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Founding bounds on a certain expression

Published on 10 May 2026 - 17:34

1.1k

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L2-norm and H2-norm

Published on 16 Apr 2026 - 14:45

158

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How can I show that the Sobolev space $W_p^1 (a,b)$ is closed?

Published on 14 Apr 2026 - 15:03

91

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Continuity of a bilinear form on $H^1(0,2)$

Published on 14 Apr 2026 - 2:47

164

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Sobolev embedding on the torus

Published on 14 Apr 2026 - 14:13

40

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$W^{2,2} \subset W^{1,p}$ for same $p > 2$?

Published on 17 Apr 2026 - 10:41

222

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Does the constant in Poincaré inequality (for $W^{1,p}_0$) depend on $p$?

Published on 14 Apr 2026 - 10:33

126

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Proving that $\{\varphi\in C^{\infty}(\Omega)\,: \varphi(b) = 0\}$ is dense in $\{u\in H^1(\Omega)\,:\, u(b) = 0\}$

Published on 14 Apr 2026 - 20:36

31

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Weak derivative in $x_3$-direction equals zero implies independence of $x_3$

Published on 16 Apr 2026 - 18:16

159

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Show that there exists a unique solution

Published on 14 Apr 2026 - 14:07

52

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Application for the trace inequality.

Published on 13 Apr 2026 - 20:58

45

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$W^{1,\infty}$ convergence vs Lipschitz convergence

Published on 19 Apr 2026 - 0:20

390

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Reference for $L^p$ estimates

Published on 15 Apr 2026 - 3:01

41

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Inequality $(\alpha f,g)_{L^2}\leq C\|\alpha\|_{W}\|f\|_{H^{1/2}}\|g\|_{H^{3/2}}$

Published on 17 Apr 2026 - 3:21

List Question

Prooving compact support on Lemma 9.2 Brézis

Founding bounds on a certain expression

L2-norm and H2-norm

How can I show that the Sobolev space $W_p^1 (a,b)$ is closed?

Continuity of a bilinear form on $H^1(0,2)$

Sobolev embedding on the torus

$W^{2,2} \subset W^{1,p}$ for same $p > 2$?

Does the constant in Poincaré inequality (for $W^{1,p}_0$) depend on $p$?

Proving that $\{\varphi\in C^{\infty}(\Omega)\,: \varphi(b) = 0\}$ is dense in $\{u\in H^1(\Omega)\,:\, u(b) = 0\}$

Weak derivative in $x_3$-direction equals zero implies independence of $x_3$

Show that there exists a unique solution

Application for the trace inequality.

$W^{1,\infty}$ convergence vs Lipschitz convergence

Reference for $L^p$ estimates

Inequality $(\alpha f,g)_{L^2}\leq C\|\alpha\|_{W}\|f\|_{H^{1/2}}\|g\|_{H^{3/2}}$

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