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Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations I: the $d$ -Concavity and the Comparison Principle

$icon-email$ Ha Tien Ngoan , Thai Thi Kim Chung

Abstract

We introduce the notion of $d$ -concavity, $d \geq 0$ , and prove that the nonsymmetric Monge-Ampère type function of matrix variable is concave in an appropriate unbounded and convex set. We prove also the comparison principle for nonsymmetric Monge-Ampère type equations in the case when they are so-called $δ$ -elliptic with respect to compared functions with $0 \leq δ < 1$ .

Acta Mathematica Vietnamica

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Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations I: the d-Concavity and the Comparison Principle

Abstract

Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations I: the $d$ -Concavity and the Comparison Principle