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Acta Mathematica Vietnamica

The Dirichlet Problem for Nonsymmetric Augmented Hessian Quotient Type Equations

icon-email Van-Bang Tran , Tien-Ngoan Ha , Huu-Tho Nguyen , Trong-Tien Phan , Hong-Quang Dinh

Abstract

We deal with the Dirichlet problem for nonsymmetric augmented Hessian quotient type equations. First, we look for an admissible solution to the problem for corresponding symmetric augmented Hessian quotient type equations. Then we apply the Banach fixed point theorem to prove the existence of a $\delta$-admissible solution in $C^{2,\alpha }$ to the problem by assuming that the augmented skew-symmetric matrix is sufficiently small in a certain sense. We also give a necessary condition for the existence and sufficient conditions for uniqueness of this kind of $\delta$-admissible solutions.

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Viện Hàn lâm Khoa học và Công nghệ Việt Nam Hội Toán học Việt Nam Viện Nghiên cứu Cao cấp về toán MathScinet Arxiv