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Maximum Principles and Aleksandrov--Bakelman--Pucci Type Estimates for NonLocal Schrödinger Equations with Exterior Conditions
We consider Dirichlet exterior value problems related to a class of nonlocal Schrödinger operators, whose kinetic terms are given in terms of Bernstein functions of the Laplacian. We prove elliptic and parabolic Aleksandrov--Bakelman--Pucci (ABP) type estimates and as an application obtain existence and uniqueness of weak solutions. Next we prove …