Holder regularity of the solution to the complex Monge-Ampere equation with L-p density

摘要

On a smooth domain Omega subset of subset of C-n, we consider the Dirichlet problem for the complex Monge-Ampere equation ((dd(c)u)(n) = fdV, u vertical bar b(Omega) phi). We state the Holder regularity of the solution u when the boundary value phi is Holder continuous and the density f is only L-p, p > 1. Note that in former literature (Guedj-Kolodziej-Zeriahi) the weakness of the assumption f is an element of L-p was balanced by taking phi is an element of C-1,C-1 (in addition to assuming Omega strongly pseudoconvex).