List questions from sobolev-spaces

Published on 29 Dec 2016 - 12:39

117

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Bounding the $L^2$ norm of a function in $H^1$

Published on 30 Dec 2016 - 6:06

377

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Cutoff and Poincare inequality

Published on 30 Dec 2016 - 11:08

20

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Do we have embedding theorem for $\mathcal{E}_{2,p}=\{u\in L^p(\Bbb R^3), \nabla u\in L^2(\Bbb R^3)\}$?

Published on 01 Jan 2017 - 3:56

70

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Banach valued functions

Published on 01 Jan 2017 - 15:25

64

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Totaly continuous embedding implies convergence of subsequence?

Published on 26 Mar 2026 - 7:57

660

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Laplace equation with Robin b.c. - weak solution, proof of coercivity

Published on 02 Jan 2017 - 20:13

47

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Is it possible to bound $\|u\|_{H^{1/2}(\partial K)}$ by $\|u\|_{L^2(\partial K)}$ for polynomial $u$?

Published on 03 Jan 2017 - 8:17

184

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Chain rule for Sobolev functions, case $p=\infty$

Published on 30 Mar 2026 - 23:21

262

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Fractional powers for the Laplacian with Dirichlet boundary conditions

Published on 29 Mar 2026 - 18:13

213

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Is $H_0^1(\Lambda)\cap H^2(\Lambda)=H_0^2(\Lambda)$ for any open $\Lambda$?

Published on 05 Jan 2017 - 18:19

45

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For which negative values of $s$ is $\delta\in W^{2,s}(\mathbb{R}^{n})$?

Published on 31 Mar 2026 - 22:46

51

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What it means $\lim_{|x|\rightarrow+\infty}u(x)=0$?

Published on 06 Jan 2017 - 17:47

135

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Do we have that $\overline{\mathcal C_0^\infty (\Omega )}=W^{1,p}(\Omega )$?

Published on 07 Jan 2017 - 14:26

44

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Concrete identification of a functional

Published on 31 Mar 2026 - 22:45

List Question

$u\in H^1(\Omega )\implies u^+,u^-,|u|\in H^1(\Omega )$.

Bounding the $L^2$ norm of a function in $H^1$

Cutoff and Poincare inequality

Do we have embedding theorem for $\mathcal{E}_{2,p}=\{u\in L^p(\Bbb R^3), \nabla u\in L^2(\Bbb R^3)\}$?

Banach valued functions

Totaly continuous embedding implies convergence of subsequence?

Laplace equation with Robin b.c. - weak solution, proof of coercivity

Is it possible to bound $\|u\|_{H^{1/2}(\partial K)}$ by $\|u\|_{L^2(\partial K)}$ for polynomial $u$?

Chain rule for Sobolev functions, case $p=\infty$

Fractional powers for the Laplacian with Dirichlet boundary conditions

Is $H_0^1(\Lambda)\cap H^2(\Lambda)=H_0^2(\Lambda)$ for any open $\Lambda$?

For which negative values of $s$ is $\delta\in W^{2,s}(\mathbb{R}^{n})$?

What it means $\lim_{|x|\rightarrow+\infty}u(x)=0$?

Do we have that $\overline{\mathcal C_0^\infty (\Omega )}=W^{1,p}(\Omega )$?

Concrete identification of a functional

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