Now showing 1 - 2 of 2
  • Publication
    Principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term
    (2020-01-01) ;
    Salort, Ariel
    ;
    Xia, Aliang
    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”.
  • Publication
    The evolution problem associated with the fractional first eigenvalue
    (2024-07-01)
    Barrios, Begoña
    ;
    Del Pezzo, Leandro
    ;
    ;
    Rossi, Julio D.
    In this paper we study the evolution problem associated with the first fractional eigenvalue. We prove that the Dirichlet problem with homogeneous boundary condition is well posed for this operator in the framework of viscosity solutions (the problem has existence and uniqueness of a solution and a comparison principle holds). In addition, we show that solutions decay to zero exponentially fast as t → ∞ with a bound that is given by the first eigenvalue for this problem that we also study