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Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations II. A Priori Estimates and the Dirichlet Problem
Ha Tien Ngoan
,
Thai Thi Kim Chung
Abstract
In this paper, we consider the Dirichlet problem for nonsymmetric Monge-Ampère type equations in which a skew-symmetric matrix is introduced. We establish uniform with respect to a class of skew-symmetric matrix bounds for $\delta$-elliptic $C^{2, \alpha }(\overline {{\Omega }})$-solutions to the Dirichlet problem. Then, we prove the classical solvability of the Dirichlet problem, provided those skew-symmetric matrices are sufficiently small in some sense.