On the existence and regularity of Dirichlet problem for complex Monge-Amp�re equationson weakly pseudoconvex domains

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

“…Proof We use the technique of Li [30] (also see [2]). By the hypotheses it implies that h ξ ∈ P SH(Ω), ∀ξ ∈ ∂Ω.…”

“…Ko lodziej [25] proved that there exists a unique continuous solution to M A(Ω, φ, f ) on strictly pseudoconvex domains. Li [30] studied the problem on a bounded pseudoconvex domain in C n with C 2 boundary. He proved that if Ω is bounded pseudoconvex domain of plurisubharmonic type m with C 2 boundary, φ ∈ C mα (∂Ω) with 0 < α ≤ 2 m and f 1 n ∈ C α (Ω) then M A(Ω, φ, f ) has a unique solution u ∈ C α (Ω).…”

“…Main purpose of this paper is to generalize the theorem of [2] from C 2 smooth bounded pseudoconvex domain of plurisubharmonic type m to nonsmooth pseudoconvex domains of plurisubharmonic type m. First we give the following definition which is an extension of Li [30] (also see [2]). Definition 1 Let m > 0 and let Ω be a pseudoconvex domain in C n .…”

Plurisubharmonicity for the solution of the Fefferman equation and applications

“…is strictly plurisubharmonic in D. It is known from [5,[14][15][16] that the following identity holds: Fefferman [6] gave a formula to approximate the potential function ρ [for Eq. (…”

An explicit formula for the Webster pseudo-Ricci curvature on real hypersurfaces and its application for characterizing balls in {$\Bbb C\sp n$}

“…We use some notations in [24] and [25]. If H(u) is invertible, then we let [u kj ] be the inverse of H(u) t so that …”