Question

When is $u \in W^{1,p}(\Omega)$?

score 37 · Answer 1 · 2017-01-29 15:42:13

37

Views

When is $u \in W^{1,p}(\Omega)$?

Published on 29 Jan 2017 - 15:42

score 164 · Answer 2 · 2026-03-29 19:08:27

164

Views

Counter example for a norm relationship

Published on 29 Mar 2026 - 19:08

score 31 · Answer 3 · 2026-04-03 01:14:58

31

Views

Function in VMO$(S^1,S^1)$

Published on 03 Apr 2026 - 1:14

score 26 · Answer 4 · 2017-01-31 04:51:00

26

Views

Show that the set of potential fields is closed in $L^2(\Omega)$.

Published on 31 Jan 2017 - 4:51

score 521 · Answer 5 · 2017-01-31 17:10:33

521

Views

Bounding Dirichlet energy for Poisson equation from below

Published on 31 Jan 2017 - 17:10

score 2k · Answer 6 · 2017-02-01 15:57:00

2k

Views

Normal derivative of a $H^1$- Sobolev function

Published on 01 Feb 2017 - 15:57

score 170 · Answer 7 · 2026-04-03 01:17:50

170

Views

Strict inclusions $H^{1/2}\subsetneq\operatorname{vmo}\subsetneq \operatorname{bmo}$ on $S^1$

Published on 03 Apr 2026 - 1:17

score 164 · Answer 8 · 2026-03-28 00:06:14

164

Views

If $u\in H_0^1$ admits a weak Laplacian in $L^2$, are we able to show $\nabla u\in L^p$ for some $p>2$?

Published on 28 Mar 2026 - 0:06

score 79 · Answer 9 · 2017-02-03 21:06:07

79

Views

Sobolev inequalities on bounded open subsets of $\mathbb R^d$ whose boundary is not $C^1$ but Lipschitz

Published on 03 Feb 2017 - 21:06

score 37 · Answer 10 · 2017-02-04 18:05:46

37

Views

Different ways of showing that $f(t)=i\int_0^t g(s)e^{-\lambda i (t-s)}\,ds$ belong to sobolev space $W_0^{1,2} (0,1)$

Published on 04 Feb 2017 - 18:05

score 365 · Answer 11 · 2026-03-28 00:06:08

365

Views

Sobolev norm of composite function

Published on 28 Mar 2026 - 0:06

score 125 · Answer 12 · 2026-03-29 20:01:25

125

Views

If $u\in H_0^1$ with $\Delta u\in L^2$, then $\left\|\Delta u\right\|_{L^2}\le C\left\|u\right\|_{H^1}$

Published on 29 Mar 2026 - 20:01

score 90 · Answer 13 · 2017-02-06 16:32:31

If there is a bounded linear extension $W^{k,\:p}(Λ)\to W^{k,\:p}(ℝ^d)$, are we able to conclude the existence of such an extension for other $k,p$?

score 28 · Answer 14 · 2017-02-06 16:51:08

If there is a bounded linear extension $W^{1,p}(Λ)\to W^{1,p}(ℝ^d)$, do the Sobolev inequalities for $W^{k,p}(ℝ^d)$ transfer over to $W^{k,p}(Λ)$?

score 87 · Answer 15 · 2026-04-01 01:58:28

87

Views

Distribution as a limit

Published on 01 Apr 2026 - 1:58

List Question

When is $u \in W^{1,p}(\Omega)$?

Counter example for a norm relationship

Function in VMO$(S^1,S^1)$

Show that the set of potential fields is closed in $L^2(\Omega)$.

Bounding Dirichlet energy for Poisson equation from below

Normal derivative of a $H^1$- Sobolev function

Strict inclusions $H^{1/2}\subsetneq\operatorname{vmo}\subsetneq \operatorname{bmo}$ on $S^1$

If $u\in H_0^1$ admits a weak Laplacian in $L^2$, are we able to show $\nabla u\in L^p$ for some $p>2$?

Sobolev inequalities on bounded open subsets of $\mathbb R^d$ whose boundary is not $C^1$ but Lipschitz

Different ways of showing that $f(t)=i\int_0^t g(s)e^{-\lambda i (t-s)}\,ds$ belong to sobolev space $W_0^{1,2} (0,1)$

Sobolev norm of composite function

If $u\in H_0^1$ with $\Delta u\in L^2$, then $\left\|\Delta u\right\|_{L^2}\le C\left\|u\right\|_{H^1}$

If there is a bounded linear extension $W^{k,\:p}(Λ)\to W^{k,\:p}(ℝ^d)$, are we able to conclude the existence of such an extension for other $k,p$?

If there is a bounded linear extension $W^{1,p}(Λ)\to W^{1,p}(ℝ^d)$, do the Sobolev inequalities for $W^{k,p}(ℝ^d)$ transfer over to $W^{k,p}(Λ)$?

Distribution as a limit

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