Resumen de The Dirichlet Problem for the Degenerate Monge-Ampère Equation.

Elena Caffarelli, Louis Nirenberg, Joel Spruck

• Let O be a bounded convex domain in Rn with smooth, strictly convex boundary ¶O, i.e. the principal curvatures of ¶O are all positive. We study the problem of finding a convex function u in O such that:

  det (uij) = 0 in O u = f given on ¶O.