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Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations I: the $d$-Concavity and the Comparison Principle
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 $\delta$-elliptic with respect to compared functions with $0 \leq \delta < 1$.