Calculus of Variations and Geometric Measure Theory
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G. Catino - D. D. Monticelli - F. Punzo

The Poisson equation on manifolds with positive essential spectrum

created by catino on 27 Mar 2018
modified on 12 Oct 2018

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Submitted Paper

Inserted: 27 mar 2018
Last Updated: 12 oct 2018

Year: 2018

Abstract:

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. We do not require any assumptions on the curvature. In particular we can allow the Ricci curvature to be unbounded from below.


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