Timeline for On which regions can Green's theorem not be applied?

7 events

when toggle format	what		by	license	comment
Jan 18, 2021 at 2:38	history	edited	David Roberts♦	CC BY-SA 4.0	Bibliographic reference
Sep 25, 2020 at 13:50	comment	added	Jules		It can be generalized even beyond subsets. A subset of the plane may be viewed as a function $f : \mathbb{R}^2 \to {0,1}$, but we can also generalize the range to be $\mathbb{R}$, to allow fractional points to be in that subset. We can then define the integral over the "generalized subset" $\int_f g$ = $\int f g$. In this case Greene's theorem becomes the same as integration by parts. Now we can generalize $f$ further from a function to a Schwartz distribution, and perhaps beyond.
Apr 27, 2020 at 20:40	comment	added	alephzero		"I'll start with my first thought: surely there's no hope of formulating Green's theorem for an unbounded region" Don't tell people solving external acoustic problems that. The entire foundation of their boundary element numerical methods is Green's functions on unbounded regions of $\mathbb{R}^3$.
Apr 27, 2020 at 18:42	comment	added	John Kemeny		"The best way to get the right answer on the Internet is not to ask a question; it's to post the wrong answer." — Ward Cunningham's law.
Apr 27, 2020 at 13:25	comment	added	Alexey Romanov		To extend the first idea: the entire plane? Or the plane except a single point?
Apr 26, 2020 at 18:54	comment	added	GermanJablo		Thank you. Your response has been very helpful.
Apr 26, 2020 at 16:32	history	answered	Paul Siegel	CC BY-SA 4.0