Question

Sobolev spaces on $B_1^2(0)$ don't change if we remove a point from the domain

score 480 · Answer 1 · 2026-04-16 13:53:17

480

Views

Sobolev spaces on $B_1^2(0)$ don't change if we remove a point from the domain

Published on 16 Apr 2026 - 13:53

score 111 · Answer 2 · 2026-04-13 04:54:12

111

Views

Does $u \in W^{1,2}_0(\Omega)$ imply $|u| \in W^{1,2}_0(\Omega)$?

Published on 13 Apr 2026 - 4:54

score 40 · Answer 3 · 2026-04-09 16:11:14

40

Views

Minimisation problem in Sobolev space

Published on 09 Apr 2026 - 16:11

score 60 · Answer 4 · 2026-03-26 20:44:35

60

Views

contunuous embedding $\mathcal{W}\subset C(0,T,V)$ and weak convergence question

Published on 26 Mar 2026 - 20:44

score 134 · Answer 5 · 2026-03-28 12:14:32

134

Views

Question on application of the dominated convergence theorem in showing that $|f|$ is weakly differentiable

Published on 28 Mar 2026 - 12:14

score 87 · Answer 6 · 2026-04-17 02:46:36

87

Views

equivalent condition in sobolev spaces

Published on 17 Apr 2026 - 2:46

score 86 · Answer 7 · 2026-04-16 07:52:00

86

Views

Convergence of a sequence $g_n(x)$ to $g(x) = 1-|x|$ in $W^{1,p}(B(0,r=1) \setminus 0)$ for $1 \le p \le 2$ , where $B(0,1) \subset \mathbb{R}^2$

Published on 16 Apr 2026 - 7:52

score 275 · Answer 8 · 2026-04-13 22:26:27

275

Views

Is the function in $W^{k,p}$ with $0$ $k$-th weak derivative a polynomial of at most $k-1$ degree?

Published on 13 Apr 2026 - 22:26

score 55 · Answer 9 · 2026-04-10 15:00:58

55

Views

This operator is it compact?

Published on 10 Apr 2026 - 15:00

score 596 · Answer 10 · 2026-04-11 20:58:58

596

Views

Convergence of mollification of a function

Published on 11 Apr 2026 - 20:58

score 88 · Answer 11 · 2026-04-14 13:01:45

88

Views

Annihilator of the image of $\Delta$ is a subset of the space of harmonic functions.

Published on 14 Apr 2026 - 13:01

score 94 · Answer 12 · 2026-04-17 07:02:56

A sequence $\{u_n\}$ in $W^{1,p}(1 <p \leq \infty)$ converges to some $u$ in $L^p$, and $\{u_n'\}$ is bounded in $L^p$. How to prove $u \in W^{1,p}$?

score 674 · Answer 13 · 2026-03-28 13:38:38

674

Views

Absolute value of a function in $W^{1,2}_0$?

Published on 28 Mar 2026 - 13:38

score 3.3k · Answer 14 · 2026-04-18 23:05:42

3.3k

Views

Intuition behind Sobolev Inequality

Published on 18 Apr 2026 - 23:05

score 33 · Answer 15 · 2026-04-16 00:42:32

33

Views

Choose $u_{m}\in W_{p}^{2}(\Omega)\cap W_{q}^{2}(\Omega)$ to harmonic function $u$.

Published on 16 Apr 2026 - 0:42

List Question

Sobolev spaces on $B_1^2(0)$ don't change if we remove a point from the domain

Does $u \in W^{1,2}_0(\Omega)$ imply $|u| \in W^{1,2}_0(\Omega)$?

Minimisation problem in Sobolev space

contunuous embedding $\mathcal{W}\subset C(0,T,V)$ and weak convergence question

Question on application of the dominated convergence theorem in showing that $|f|$ is weakly differentiable

equivalent condition in sobolev spaces

Convergence of a sequence $g_n(x)$ to $g(x) = 1-|x|$ in $W^{1,p}(B(0,r=1) \setminus 0)$ for $1 \le p \le 2$ , where $B(0,1) \subset \mathbb{R}^2$

Is the function in $W^{k,p}$ with $0$ $k$-th weak derivative a polynomial of at most $k-1$ degree?

This operator is it compact?

Convergence of mollification of a function

Annihilator of the image of $\Delta$ is a subset of the space of harmonic functions.

A sequence $\{u_n\}$ in $W^{1,p}(1 <p \leq \infty)$ converges to some $u$ in $L^p$, and $\{u_n'\}$ is bounded in $L^p$. How to prove $u \in W^{1,p}$?

Absolute value of a function in $W^{1,2}_0$?

Intuition behind Sobolev Inequality

Choose $u_{m}\in W_{p}^{2}(\Omega)\cap W_{q}^{2}(\Omega)$ to harmonic function $u$.

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