Question

Are $\| \Delta u \|_{L^p(\Bbb R^d)} + \| u \|_{L^p(\Bbb R^d)}~~and\| u \|_{W^{2,p}(\Bbb R^d)}$ equivalents norms?

score 81 · Answer 1 · 2026-03-27 19:33:42

81

Views

Are $\| \Delta u \|_{L^p(\Bbb R^d)} + \| u \|_{L^p(\Bbb R^d)}~~and\| u \|_{W^{2,p}(\Bbb R^d)}$ equivalents norms?

Published on 27 Mar 2026 - 19:33

score 619 · Answer 2 · 2026-04-13 19:22:39

619

Views

class of compact support functions is dense in $W^{k,p}(\mathbb R^n)$

Published on 13 Apr 2026 - 19:22

score 471 · Answer 3 · 2026-04-14 23:33:35

471

Views

counter-example for the Poincaré's inequality

Published on 14 Apr 2026 - 23:33

score 87 · Answer 4 · 2026-04-14 15:16:00

87

Views

The multiplicative property of the Sobolev spaces.

Published on 14 Apr 2026 - 15:16

score 195 · Answer 5 · 2026-04-15 05:53:30

195

Views

Schwartz space on $\mathbb{R}^{n}$ and ring of derivations

Published on 15 Apr 2026 - 5:53

score 200 · Answer 6 · 2026-04-11 16:38:20

200

Views

Statement about Lipschitz functions

Published on 11 Apr 2026 - 16:38

score 933 · Answer 7 · 2026-03-28 11:53:28

933

Views

Weak convergence of weak derivatives.

Published on 28 Mar 2026 - 11:53

score 196 · Answer 8 · 2026-03-28 01:06:12

196

Views

Boundary value problem with Neumann boundary conditions

Published on 28 Mar 2026 - 1:06

score 34 · Answer 9 · 2026-04-14 07:35:41

34

Views

Subsequence in $W^{1,1}$

Published on 14 Apr 2026 - 7:35

score 1.9k · Answer 10 · 2026-04-13 05:01:13

1.9k

Views

If $u\in H^1(\Omega )$ then $|u|\in H^1(\Omega )$.

Published on 13 Apr 2026 - 5:01

score 41 · Answer 11 · 2026-03-26 03:10:50

41

Views

how to understand this operator

Published on 26 Mar 2026 - 3:10

score 312 · Answer 12 · 2026-04-16 13:44:54

312

Views

Show that $\mathcal C^1(\bar \Omega )$ is dense in $W^{1,p}(\Omega )$.

Published on 16 Apr 2026 - 13:44

score 51 · Answer 13 · 2026-04-16 13:48:21

51

Views

Show there is $C$ independent of $u$ s.t. $\|u-\bar u\|_{L^p(B_1)}\leq C\|\nabla u\|_{L^p(B_1)}$.

Published on 16 Apr 2026 - 13:48

score 95 · Answer 14 · 2026-04-15 09:57:21

95

Views

$\nabla u=0$ implies $u$ is constant everywhere or almost everywhere?

Published on 15 Apr 2026 - 9:57

score 55 · Answer 15 · 2026-04-15 06:19:27

55

Views

If $(u_n) \subset W^{1,p}(\Omega )$. If $u_n\to u$ strongly and $\nabla u_n \to v$ weakly, does $v=\nabla u$?

Published on 15 Apr 2026 - 6:19

List Question

Are $\| \Delta u \|_{L^p(\Bbb R^d)} + \| u \|_{L^p(\Bbb R^d)}~~and\| u \|_{W^{2,p}(\Bbb R^d)}$ equivalents norms?

class of compact support functions is dense in $W^{k,p}(\mathbb R^n)$

counter-example for the Poincaré's inequality

The multiplicative property of the Sobolev spaces.

Schwartz space on $\mathbb{R}^{n}$ and ring of derivations

Statement about Lipschitz functions

Weak convergence of weak derivatives.

Boundary value problem with Neumann boundary conditions

Subsequence in $W^{1,1}$

If $u\in H^1(\Omega )$ then $|u|\in H^1(\Omega )$.

how to understand this operator

Show that $\mathcal C^1(\bar \Omega )$ is dense in $W^{1,p}(\Omega )$.

Show there is $C$ independent of $u$ s.t. $\|u-\bar u\|_{L^p(B_1)}\leq C\|\nabla u\|_{L^p(B_1)}$.

$\nabla u=0$ implies $u$ is constant everywhere or almost everywhere?

If $(u_n) \subset W^{1,p}(\Omega )$. If $u_n\to u$ strongly and $\nabla u_n \to v$ weakly, does $v=\nabla u$?

Trending Questions

Popular # Hahtags

Popular Questions