637 reputation
214
bio website
location
age
visits member for 2 years, 9 months
seen Nov 8 at 20:09

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?
Apr
8
revised Approximating measurable function by continuous ones
deleted 49 characters in body
Apr
8
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.
Apr
8
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)
Apr
7
revised approximate measurable function by continuous ones
deleted 59 characters in body
Apr
7
asked approximate measurable function by continuous ones
Apr
7
asked Approximating measurable function by continuous ones
Mar
13
awarded  Yearling
Feb
11
accepted Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
Feb
10
comment Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
I've actually been looking at this proof at a more careful level. And I realized Tubular Neighborhood and Retraction are exactly the tools that Lee used to solve the question I have. I guess I will choose @Potato as the best answer if nobody gives a better answer in the following couple of days! Thanks man, @Potato!
Feb
9
comment Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
I saw this proof before. But since I am not aware of Whitney approximation theorem or the smooth retraction mentioned in the proof, I skipped it. Bott, Tu's book's proof requires less background knowledge. But as I explained, I found I can't get around that point. I still wish that someone might be able to tell me how it is possible.
Feb
9
asked Approximate continuous mapping by smooth mappings on manifold(Bott, Tu book)
Nov
20
awarded  Critic
Nov
20
awarded  Supporter