Question

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

score 34 · Answer 1 · 2026-03-25 03:04:10

34

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

Published on 25 Mar 2026 - 3:04

score 94 · Answer 2 · 2026-03-22 20:19:29

94

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

Published on 22 Mar 2026 - 20:19

score 63 · Answer 3 · 2026-03-20 06:21:46

63

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

Published on 20 Mar 2026 - 6:21

score 341 · Answer 4 · 2026-03-24 20:33:23

341

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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 24 Mar 2026 - 20:33

score 218 · Answer 5 · 2018-01-29 18:08:00

218

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

Published on 29 Jan 2018 - 18:08

score 71 · Answer 6 · 2026-03-22 21:44:15

71

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

Published on 22 Mar 2026 - 21:44

score 457 · Answer 7 · 2026-03-23 12:30:37

457

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

Published on 23 Mar 2026 - 12:30

score 523 · Answer 8 · 2026-03-22 23:08:35

523

Views

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

Published on 22 Mar 2026 - 23:08

score 128 · Answer 9 · 2026-03-26 03:56:21

128

Views

Regularity of the Divergence of Weak Solutions to Elliptic PDEs

Published on 26 Mar 2026 - 3:56

score 115 · Answer 10 · 2026-03-24 23:59:20

115

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Book references for extensive self study

Published on 24 Mar 2026 - 23:59

score 122 · Answer 11 · 2026-03-17 11:18:45

122

Views

Implications of weak convergence on the Lebesgue space to Sobolev space

Published on 17 Mar 2026 - 11:18

score 454 · Answer 12 · 2026-03-20 09:43:04

454

Views

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

Published on 20 Mar 2026 - 9:43

score 33 · Answer 13 · 2018-02-02 14:39:13

33

Views

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 02 Feb 2018 - 14:39

score 138 · Answer 14 · 2026-03-17 22:39:31

138

Views

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

Published on 17 Mar 2026 - 22:39

score 48 · Answer 15 · 2026-03-22 19:50:40

48

Views

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

Published on 22 Mar 2026 - 19:50

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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