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1h
comment Help with proof that $H^{1}(\mathbb{R})$ is closed under multiplication.
As noted on the comments of OP's question, the same result is not true for $N>1$, however, a sufficient condition for $uv\in H^1(\Omega)$, when $u,v\in H^1(\Omega)$ and $\Omega$ is an open set, is that $u,v\in L^\infty(\Omega)$.
1h
answered Help with proof that $H^{1}(\mathbb{R})$ is closed under multiplication.
2d
answered Basic question about weak solution of p-Laplace equation
2d
comment Basic question about weak solution of p-Laplace equation
It is the operator $p$ Laplacean or just the Laplacean? Your interpretation of weak solution for the $p$ Laplacean is nor right, it is missign the term $|\nabla u|^{p-2}$.
Dec
15
comment Spaces of the derivative in a direction
What do you mean by $\phi=L^p(\Omega)\to \mathbb{R}$. Your question suggests that $\phi:H_0^1(\Omega)\to \mathbb{R}$. Is that right?
Dec
13
comment Calculate weak derivative
The weak derivative must belong to $L^1_{loc}$, so only redefining it in a set of zero measure, is not sufficient to solve the problem.
Dec
11
comment Is fractional order Sobolev spaces reflexive?
You are welcome @liuwul000
Dec
11
comment Is the following function absolutely continuous?.
I am trying to write a proof. The idea I am trying to use, is that near $x$, your function is $1$ and so it is Lipschitz. Far from $x$ your function is also Lipschitz, because the funtcion $|x-y|^2$ is bounded if $y$ is far from $x$ and the distance function is Lipschitz.
Dec
11
comment Is the following function absolutely continuous?.
It seems to me that this function is Lipschitz. Where do you got this problem?
Dec
11
answered Is fractional order Sobolev spaces reflexive?
Dec
9
awarded  Caucus
Dec
7
comment The distance from the center of a circle, which is tangent to a ellipse $x^2/a^2+y^2/b^2=1$ and two parallel tangent lines of the ellipse is $a+b$
Can you read Russian? I entered in Prasolov's page and I downloaded the book, however, I can't find nothing on it. Maybe there is some reference there.
Nov
28
reviewed Approve The distance from the center of a circle, which is tangent to a ellipse $x^2/a^2+y^2/b^2=1$ and two parallel tangent lines of the ellipse is $a+b$
Nov
28
asked The distance from the center of a circle, which is tangent to a ellipse $x^2/a^2+y^2/b^2=1$ and two parallel tangent lines of the ellipse is $a+b$
Nov
25
comment Weak subsolution and composition with convex smooth function
I fail to see why the third equality is true. Also, check here
Nov
25
comment weak subsolution
I don't see the point of your comment @TKM
Nov
25
answered Trace on $H^1(\Omega_1\cup\Omega_2)$ (one little question in the conclusion of my proof)
Nov
18
comment Weak convergence of determinant
Maybe this is not true. Take a look in this answer. Maybe with some adaptation, it is possible to give a conter example for your problem. I was thinking in defining $u_n=(\cos(nx)/n,\cos(nx)/n)$.
Nov
5
awarded  Nice Question
Nov
5
comment Isolated singularity of harmonic function
Ok, now to conclude, you can use the fact that $\epsilon$ is arbitrary, therefore, $|u(x)-v(x)|\le 0$ for all $x$ in the ball.