Boundary Behavior of Large Solutions to the Monge-Ampère Equation in a Borderline Case.

This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampère equation detD2u(x) = b(x)f (u(x)), u > 0, x ∈ Ω, where Ω is a strictly convex and bounded smooth domain in ℝN with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b ∈ C∞ (Ω) is positive in Ω, but may be appropriate singular on the boundary. [ABSTRACT FROM AUTHOR]