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 R n ( n ≥ 2 ) with prescribed asymptotic behavior at infinity. This extends the Caffarelli–Li’s result on det ( D 2 u ) = 1 . We also obtain the existence of entire convex viscosity solutions to the Monge–Ampère equations with prescribed asymptotic behavior at infinity.