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  • 7 votes cast
Apr
6
comment proof on Poincare's inequality.
which notation do you need me to explain?
Apr
6
asked proof on Poincare's inequality.
Apr
5
accepted Minimizing sequence that has certain property
Apr
3
asked Minimizing sequence that has certain property
Mar
30
accepted Limiting argument when proving inequality in Sobolev space
Mar
29
comment Limiting argument when proving inequality in Sobolev space
this makes a hell lot more sense!! Thanks!
Mar
29
comment Limiting argument when proving inequality in Sobolev space
So I should interpret this inequality as: For any $f$ in $W^{1,1}$, there is a $\tilde{f}$, s.t. $\tilde{f}=f$ in the distributional sense with $\tilde{f}\in L^{\infty}$ and that inequality holds. Am I right?
Mar
29
comment Limiting argument when proving inequality in Sobolev space
first thank you for pointing out the Cauchy sequence part. I was stupid to not have seen this. But why does $f_n$ necessarily converge to this same $f$ in $L^{\infty}$?
Mar
29
asked Limiting argument when proving inequality in Sobolev space
Mar
26
awarded  Popular Question
Mar
21
accepted What does it mean for a distribution to be in $L_2$?
Mar
21
comment What does it mean for a distribution to be in $L_2$?
I am trying to get a little intuition here. So based on what you said, a lot of distributions are not in $L_2$ since for a general distribution, you are not even lucky enough to get that kind of representation. Am I right?
Mar
21
asked What does it mean for a distribution to be in $L_2$?
Mar
13
awarded  Yearling
Feb
10
comment What is the characteristics for the wave equation with space dimension more than 1?
What do you mean by there are no characteristics in higher spatial dimensions? I thought we need to just find a function $\phi(t,x,y)$, s.t. $\phi_t^2=\phi_x^2+\phi_y^2$. And the set$\{\phi=const\}$ would be the family of characteristic surfaces. When I tried to solve the equation, I got planes. But my intuition tells me that it should be something like the cone you mentioned. I don't know where I went wrong.
Feb
10
asked What is the characteristics for the wave equation with space dimension more than 1?
Jan
24
awarded  Popular Question
Jan
21
awarded  Nice Question
Oct
12
asked how to prove this function is harmonic (Fritz John 4.1 #5)
Apr
8
comment Approximating measurable function by continuous ones
@GiuseppeNegro I did check on that one. But isn't regularity of the measure needed there?