Harnack inequality for the fractional nonlocal linearized Monge--Amp\`ere equation

TL;DR

This paper introduces the fractional nonlocal linearized Monge--Ampère equation and establishes a Harnack inequality for its solutions, extending classical PDE results to a nonlocal, fractional setting.

Contribution

The paper presents the first Harnack inequality for solutions to the fractional nonlocal linearized Monge--Ampère equation, advancing the understanding of nonlocal Monge--Ampère problems.

Findings

Proved a Harnack inequality for nonnegative solutions

Extended classical PDE results to fractional nonlocal equations

Established foundational results for fractional Monge--Ampère equations

Abstract

The fractional nonlocal linearized Monge--Amp\`ere equation is introduced. A Harnack inequality for nonnegative solutions to the Poisson problem on Monge--Amp\`ere sections is proved.