Boundary behavior of large solutions to the Monge–Ampère equations with weights

This paper is concerned with the Monge–Ampère equation detD2u(x)=b(x)f(u(x)), x∈Ωx∈Ω, where Ω is a strictly convex, bounded smooth domain in RNRN with N≥2N≥2, and b∈C∞(Ω¯) which is positive in Ω, but may be vanishing on the boundary. We find a new structure condition on f which plays a crucial role in the boundary behavior of strictly convex large solutions. Our results are obtained in a more general setting than those in Cîrstea and Trombetti (2008) [12], where f   is regularly varying at infinity with index p>Np>N.