List questions from sobolev-spaces

Published on 26 Mar 2026 - 1:09

61

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For $u\in H^s(\mathbb{R})$ with $s>n/2$, show that $\lim_{x\to\infty}u(x)=0$

Published on 14 Nov 2014 - 12:14

169

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How do we define fractional Sobolev spaces on manifolds?

Published on 15 Nov 2014 - 21:17

214

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Energy functional in Sobolev Space

Published on 19 Nov 2014 - 17:26

120

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Sobolev space $W^{1,2}((0,1))$ and boundary ODE - how does integration by parts goes?

Published on 19 Nov 2014 - 17:47

1k

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The derivative of total variation

Published on 26 Mar 2026 - 7:33

184

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Holder continuity using Sobolev imbedding

Published on 25 Mar 2026 - 12:13

30

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A $L^1$-bounded sequence from a $H^m$-bounded sequence

Published on 23 Nov 2014 - 1:21

349

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Poincare Inequality for 1-Dimensional Problem.

Published on 23 Nov 2014 - 3:37

4.9k

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Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$.

Published on 31 Mar 2026 - 8:12

310

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Proving continuity on Sobolev space with weak topology

Published on 24 Nov 2014 - 21:58

159

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For which $s$ is the function $(||x||^{s-2}x_i)^2$ integrable on the unit ball of $\mathbb R^n$?

Published on 25 Nov 2014 - 1:42

482

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Weak subsolution and composition with convex smooth function

Published on 25 Nov 2014 - 2:08

50

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Trace on $H^1(\Omega_1\cup\Omega_2)$ (one little question in the conclusion of my proof)

Published on 25 Nov 2014 - 12:18

764

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Question about difference quotient in Sobolev space

Published on 26 Nov 2014 - 1:01

List Question

divergence form of the determinant

For $u\in H^s(\mathbb{R})$ with $s>n/2$, show that $\lim_{x\to\infty}u(x)=0$

How do we define fractional Sobolev spaces on manifolds?

Energy functional in Sobolev Space

Sobolev space $W^{1,2}((0,1))$ and boundary ODE - how does integration by parts goes?

The derivative of total variation

Holder continuity using Sobolev imbedding

A $L^1$-bounded sequence from a $H^m$-bounded sequence

Poincare Inequality for 1-Dimensional Problem.

Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$.

Proving continuity on Sobolev space with weak topology

For which $s$ is the function $(||x||^{s-2}x_i)^2$ integrable on the unit ball of $\mathbb R^n$?

Weak subsolution and composition with convex smooth function

Trace on $H^1(\Omega_1\cup\Omega_2)$ (one little question in the conclusion of my proof)

Question about difference quotient in Sobolev space

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