Question

Inequality $||\theta_x||_{L^{\infty}}+||\mathcal{H}\theta_x||_{L^{\infty}}\leq C ||\theta||_{H^{2}}$

score 36 · Answer 1 · 2026-04-14 13:04:39

36

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Inequality $||\theta_x||_{L^{\infty}}+||\mathcal{H}\theta_x||_{L^{\infty}}\leq C ||\theta||_{H^{2}}$

Published on 14 Apr 2026 - 13:04

score 103 · Answer 2 · 2026-04-28 09:21:39

103

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For which functions $u$ is $\partial_\nu u \in H^{-1/ 2}(\partial\Omega)$?

Published on 28 Apr 2026 - 9:21

score 70 · Answer 3 · 2026-04-29 12:47:10

70

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If $q>p$ then $H^q([0,2\pi])$ is dense in $H^p([0,2\pi])$>

Published on 29 Apr 2026 - 12:47

score 346 · Answer 4 · 2026-04-29 12:42:58

346

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How interpret $\||x|^\gamma u\|_{L^r}\leq C\|\nabla u\|_{L^p}^{a}\||x|^\beta u\|_{L^q}^{1-a}$ for $u\in\mathcal C_0^1(\mathbb R^d)$?

Published on 29 Apr 2026 - 12:42

score 221 · Answer 5 · 2026-04-12 16:01:30

221

Views

Exercise on showing that a function with a jump discontinuity must have infinite energy

Published on 12 Apr 2026 - 16:01

score 77 · Answer 6 · 2026-04-29 12:51:04

77

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Does $(q,\nabla u)\lesssim C|u|_1$ implies $\Vert q\Vert_0\lesssim C$?

Published on 29 Apr 2026 - 12:51

score 463 · Answer 7 · 2026-05-03 08:50:23

463

Views

Find a constant to bound laplacian norm by gradient norm in finite dimension

Published on 03 May 2026 - 8:50

score 533 · Answer 8 · 2026-05-05 04:15:22

533

Views

Is the square of an $H^1$ function also $H^1$?

Published on 05 May 2026 - 4:15

score 136 · Answer 9 · 2026-05-03 08:54:28

136

Views

Regularity of the Divergence of Weak Solutions to Elliptic PDEs

Published on 03 May 2026 - 8:54

score 118 · Answer 10 · 2026-04-14 04:38:00

118

Views

Book references for extensive self study

Published on 14 Apr 2026 - 4:38

score 127 · Answer 11 · 2026-05-05 01:51:51

127

Views

Implications of weak convergence on the Lebesgue space to Sobolev space

Published on 05 May 2026 - 1:51

score 462 · Answer 12 · 2026-05-07 12:48:08

462

Views

Extension of Luzin N-property of absolutely continuous functions and measure preserving mappings

Published on 07 May 2026 - 12:48

score 36 · Answer 13 · 2026-04-15 00:37:21

36

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If $u\in \mathcal C_c^\infty (\mathbb R^d)$ does $|u|^a\in W^{1,p}$ if $a>0$ for $p\geq 1$?

Published on 15 Apr 2026 - 0:37

score 141 · Answer 14 · 2026-04-10 20:09:51

141

Views

Proving density of $H^2(\mathbb{R})$ in $L^2(\mathbb{R})$ .

Published on 10 Apr 2026 - 20:09

score 56 · Answer 15 · 2026-05-07 13:42:59

56

Views

Proving $||u_h||_1^2=(f,u_h)$ for mixed finite elements

Published on 07 May 2026 - 13:42

List Question

Inequality $||\theta_x||_{L^{\infty}}+||\mathcal{H}\theta_x||_{L^{\infty}}\leq C ||\theta||_{H^{2}}$

For which functions $u$ is $\partial_\nu u \in H^{-1/ 2}(\partial\Omega)$?

If $q>p$ then $H^q([0,2\pi])$ is dense in $H^p([0,2\pi])$>

How interpret $\||x|^\gamma u\|_{L^r}\leq C\|\nabla u\|_{L^p}^{a}\||x|^\beta u\|_{L^q}^{1-a}$ for $u\in\mathcal C_0^1(\mathbb R^d)$?

Exercise on showing that a function with a jump discontinuity must have infinite energy

Does $(q,\nabla u)\lesssim C|u|_1$ implies $\Vert q\Vert_0\lesssim C$?

Find a constant to bound laplacian norm by gradient norm in finite dimension

Is the square of an $H^1$ function also $H^1$?

Regularity of the Divergence of Weak Solutions to Elliptic PDEs

Book references for extensive self study

Implications of weak convergence on the Lebesgue space to Sobolev space

Extension of Luzin N-property of absolutely continuous functions and measure preserving mappings

If $u\in \mathcal C_c^\infty (\mathbb R^d)$ does $|u|^a\in W^{1,p}$ if $a>0$ for $p\geq 1$?

Proving density of $H^2(\mathbb{R})$ in $L^2(\mathbb{R})$ .

Proving $||u_h||_1^2=(f,u_h)$ for mixed finite elements

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