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 δ-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.
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Ngoan, H.T., Chung, T.T.K. Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations II. A Priori Estimates and the Dirichlet Problem. Acta Math Vietnam 44, 723–749 (2019). https://doi.org/10.1007/s40306-018-0270-3
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DOI: https://doi.org/10.1007/s40306-018-0270-3