A non local Monge-Ampere equation
Luis Caffarelli, Luis Silvestre
TL;DR
This paper introduces a non-local version of the Monge-Ampere operator, explores its properties, and proves the existence of C 1,1 solutions for a related global problem in the entire space.
Contribution
It presents a novel non-local Monge-Ampere operator and establishes foundational properties and solution existence results.
Findings
Defined a non-local Monge-Ampere operator
Proved properties of the operator
Established existence of C 1,1 solutions in full space
Abstract
We introduce a non local analog to the Monge-Ampere operator and show some of its properties. We prove that a global problem involving this operator has C 1,1 solutions in the full space.
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