On the exterior Dirichlet problem for Monge–Ampère equations

In this paper, we use the Perron method to prove the existence of viscosity solutions to a class of Monge–Ampère equations on exterior domains in Rn(n≥2)Rn(n≥2) with prescribed asymptotic behavior at infinity. This extends the Caffarelli–Li’s result on det(D2u)=1det(D2u)=1. We also obtain the existence of entire convex viscosity solutions to the Monge–Ampère equations with prescribed asymptotic behavior at infinity.