Principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term

TL;DR

This paper investigates the existence and uniqueness of principal eigenvalues and eigenfunctions for fully nonlinear integro-differential elliptic equations with a drift term, using advanced mathematical tools like the Krein-Rutman theorem and nonlocal ABP estimates.

Contribution

It establishes the existence, simplicity, and regularity of principal eigenvalues and eigenfunctions for a class of nonlinear integro-differential equations with drift, extending previous results to nonlocal operators.

Findings

Existence of principal eigenvalues proved using the Krein-Rutman theorem.

Eigenfunctions are shown to be simple in the viscosity sense.

Regularity results for viscosity solutions up to the boundary.

Abstract

We study existence of principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term via the Krein-Rutman theorem which based on regularity up to boundary of viscosity solutions. We also show the simplicity of the eigenfunctions in viscosity sense by a nonlocal version of ABP estimate.