Hölder continuous solutions to the complex Monge–Ampère equations in non-smooth pseudoconvex domains

Abstract

In this paper, we prove the Hölder continuity for solutions to the complex Monge-Ampère equations on non-smooth pseudoconvex domains of plurisubharmonic type m.

Local Hölder continuity of solutions of the complex Monge-Ampère equation

“…There is a very important result due to Guedj, Kołodziej and Zeriahi that the problem is solvable for class of measure µ f with f ∈ L p , p > 1 (see [11]). Recently, several other authors have used the technique of [11] to study the problem M(Ω, µ f ) for some subclasses of the class of pseudoconvex domains (see [2], [5], [17], etc). In the case of manifolds, the problem is studied by [9], [12] and some other authors.…”