ON THE BLOW-UP BOUNDARY SOLUTIONS OF THE MONGE -AMPERE EQUATION WITH SINGULAR WEIGHTS

We consider the Monge-Ampere equations detD(2)u = K(x)f(u) in Omega, with u vertical bar partial derivative Omega = +infinity, where Omega is a bounded and strictly convex smooth domain in R-N. When f(u) = e(u) or f(u) = u(P), p > N, and the weight K(x) is an element of C-infinity(Omega) grows like a negative power of d(x) = dist(x, partial derivative Omega) near partial derivative Omega, we show some results on the uniqueness, nonexistence and exact boundary blow-up rate of strictly convex solutions for this problem. Existence of such solutions will be also studied in a more general case.