Degenerate Elliptic Second-Order Equation Operator

Let $n\ge1$ be a natural number, let $U\subseteq\mathbb{R}^n$ be an open subset of Euclidean space $\mathbb{R}^n$, let $\mathbb{R}$ be the set of real numbers with the order $\le$ of its ordered field structure, let $\mathcal{S}(n)$ be the set of symmetric real $n\times n$ matrices, and let $F$ be a second-order equation operator on $U$.

We say that $F$ is degenerate elliptic if for every $x\in U$, every $r\in\mathbb{R}$, every $p\in\mathbb{R}^n$, and all $X,Y\in\mathcal{S}(n)$ satisfying $X\preceq Y$ in the positive semidefinite ordering on symmetric matrices,