I just discovered that the Chinese shop across from my office offers Szechuan style roasted peanuts, a personal favorite the unavailability of which has plagued me for years.
@Danu I hadn't heard of that result by that name, but it's the contrapositive that's important. Namely a symmetric op with domain = whole space is unbounded
So you have to work with unbounded operators
(I read the wiki article a few hours ago so maybe they said it that way, not sure)
i meant bounded above, actually
It's automatically bounded. So you have to work with densely defined operators.
@0celo7 I'm pretty sure you're trolling me---in either case the use of the word "fuck" has been discussed before. I'm pretty sure that, as long as you do not use directly at a person (like "fuck you" or "you're a fucking moron"), it's not a problem.
If you use the word "fucking" in the above sense "[X] is fucking awesome" (where X is not a potentially offensive thing---something like "linear algebra", maybe?) I'm pretty sure you're going to be okay
Hopefully, after next semester, I will understand PDEs algebraically :P (there's a course on D-modules here, but we didn't make it to actually learning how they encode differential equations this semester)
@Danu I'm currently trying to understand elliptic regularity on manifolds. The problem is that the literature has a bad habit of referencing books that do PDE on $\Bbb R^n$.
Of course, you can say "work in charts," but there's a lot of details swept under the rug in that statement.
@Danu Consider that the existence of zero modes of the Laplacian is a global property (each zero mode is a harmonic form, hence a distinct cohomology class) and you see that PDEs contain highly non-local information
@Danu So there's two parts. The first is figuring out if your PDE has any weak solutions. The second part is figuring out if the weak solution is in fact regular.