Yeah. @Mike, so we just define the map by how it operates on the basis vectors, like normal. I feel like there should be another way, but I guess it would be less concrete.
On the first day though, he did tell us essentially what we'd be doing: 1) Variationsl Metgods: gradient estimates, weak compactness. 2) Regukarity Tgeory: maximum principle, DeGiorgi-Nash-Noser Theorem. 3) Model equations: equation of constant scalar curvature of surfaces, geometric flows (heat equation).
So basically, functional analysis applied to PDEs. Most if the people in my class went to really good undergrad schools, so they've probably seen a lot of this before. I think differential geometry or analytic geometry might be his area if research?
The norm on a Sobolev space is defined analogously to the $p$-norm: take the $p$-norm of all of the derivatives, and then sum the $p$th power of these norms and take the $p$th root
I'm actually not registered for this one for a grade, though, b/c I didn't think I'm ready for it. Last semester, I took Analysis & Probability I (yes, they combined them into one course; stupid idea) and got an A-
Hi, someone can explain me hagen's answer here :http://math.stackexchange.com/questions/681051/convergence-of-a-sequence-with-x-n2-is-non-increasing I don't understand why if M is finite then all $x_n$ have the same sign? thanks
@robjohn have you ever met this integral before? $$\int_0^1 \int_{y}^{1} y\left\{\frac{x}{y}\right\}\left\{\frac{1}{x}\right\} \ dx \ dy$$ I'm still working on the triple version and wonder if here there might be found a nice way here.
Solving the integral from this answer http://math.stackexchange.com/a/558148/18908 gives me \begin{align*} = \frac{\log (2a^2)}{a} \bigl[ \arctan n + \arctan m\bigr] \end{align*}
Hello all! Let's assume that we have an $n$-dimensional Gaussian distribution with pdf $f(\mathbf{x})$. And let $H$ an $n$-dimensional hyperplane. What is the mean distance of some point in $\mathbb{R}^n$ from the hyperplane? Thanks!
@robjohn I finally put the monster in knees. It's simply down. Could you check pls some of my work while working on the last part (meaning to put on paper the details)? Now or later ... as you want.
