The Poisson equation on manifolds with positive essential spectrum

We show existence of solutions to the Poisson equation on Riemannian manifolds with positive essential spectrum, assuming a sharp pointwise decay on the source function. In particular we can allow the Ricci curvature to be unbounded from below. In comparison with previous works, we can deal with a m...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Catino, Giovanni, Dario Daniele Monticelli, Punzo, Fabio
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.06.2019
Subjects
Curvature
Poisson equation
Riemann manifold
Online AccessGet full text

Cover

More Information
Summary:We show existence of solutions to the Poisson equation on Riemannian manifolds with positive essential spectrum, assuming a sharp pointwise decay on the source function. In particular we can allow the Ricci curvature to be unbounded from below. In comparison with previous works, we can deal with a more general setting both on the spectrum and on the curvature bounds.
ISSN:2331-8422