Principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 36.

We study existence of principal eigenvalues of a fully nonlinear integro-differential elliptic equations with a drift term via the Krein–Rutman theorem and regularity estimates up to boundary of viscosity solutions. We also show simplicity of eigenfunctions in the viscosity sense by using a nonlocal version of the ABP estimate and a “sweeping lemma”.

DOI : 10.1051/cocv/2020003
Classification : 35J60, 47G20, 35P30
Mots-clés : Principal eigenvalue, integro-differential equation, regularity, Krein–Rutman theorem 
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     publisher = {EDP-Sciences},
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Quaas, Alexander; Salort, Ariel; Xia, Aliang. Principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 36. doi : 10.1051/cocv/2020003. http://www.numdam.org/articles/10.1051/cocv/2020003/

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