henryforever14
Reputation
676
Top tag
Next privilege 1,000 Rep.
Create tags
 Mar29 comment Limiting argument when proving inequality in Sobolev space this makes a hell lot more sense!! Thanks! Mar29 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? Mar29 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 $L^{\infty}$? Mar29 asked Limiting argument when proving inequality in Sobolev space Mar26 awarded Popular Question Mar21 accepted What does it mean for a distribution to be in $L_2$? Mar21 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? Mar21 asked What does it mean for a distribution to be in $L_2$? Mar13 awarded Yearling Feb10 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. Feb10 asked What is the characteristics for the wave equation with space dimension more than 1? Jan24 awarded Popular Question Jan21 awarded Nice Question Oct12 asked how to prove this function is harmonic (Fritz John 4.1 #5) Apr8 comment Approximating measurable function by continuous ones @GiuseppeNegro I did check on that one. But isn't regularity of the measure needed there? Apr8 revised Approximating measurable function by continuous ones deleted 49 characters in body Apr8 comment Approximating measurable function by continuous ones @DavideGiraudo Let's say $X$ is $\mathbb{R}^n$ with the usual topology. And sorry that I made a mistake in my original problem. I should ask for almost everywhere convergence. Apr8 comment Steiner symmetrization preserves area? This is just by the construction of Steiner symmetric action and Fubini's theorem( where you can get: in order to get area, you integrate length of chords with respect to proper measure) Apr7 asked Approximating measurable function by continuous ones Mar13 awarded Yearling