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We study a Dirichlet problem in the entire space for some nonlocal degenerateelliptic operators with internal nonlinearities. With very mild assumptions onthe boundary datum, we prove existence and uniqueness of the solution in theviscosity sense. If we further assume uniform ellipticity then the solution isshown to be classical, and even smooth if both the operator and the boundarydatum are smooth.

A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity