Timeline for On elliptic operators on non-compact manifolds

6 events

when toggle format	what		by	license	comment
Aug 1 at 21:34	answer	added	Bazin		timeline score: 2
Aug 1 at 12:12	comment	added	Tobias Diez		I don't have a copy of the book at hand to check myself, but you may try Eichhorn's "Global analysis on open manifolds".
Aug 1 at 7:05	comment	added	G. Blaickner		@IgorKhavkine Thanks a lot for your comment! Thats indeed interesting, but unfortunately, not quite what I am looking for. I am a bit suprised that there seems to be no general result. At least for the Poisson equation on complete manifold, I think I have seen the claim somewhere that there is a Green's function $G:C^{\infty}_{c}(M)\to L^{2}(M)$, but I might be wrong though.
Jul 30 at 23:56	comment	added	Igor Khavkine		FYI, the general results in Malgrange's article don't depend on any Riemannian metric, so there is no natural $L^2(M)$ space on them. The closest result that might be of interest to you seems to be Thm.III.5: $D\colon H_{loc}^k(M) \to H_{loc}^{k-m}(M)$ is surjective, where the function spaces are local Sobolev ($k=\pm \infty$ are allowed), $m$ is the degree of $D$, and $D$ is both elliptic and has analytic coefficients. He later shows that the existence of a fundamental solution follows, but again without any global $L^2(M)$ properties.
Jul 30 at 13:12	history	edited	G. Blaickner	CC BY-SA 4.0	added 5 characters in body
Jul 30 at 13:06	history	asked	G. Blaickner	CC BY-SA 4.0