Is there a way to describe the set of strongly elliptic functions
$$ A:=\{a:\mathbb{R}^n\to\mathbb{R}^n\mid\forall x,y\in \mathbb{R}^n,\ (a(x)-a(y))\cdot(x-y)\ge K\|x-y\|^2 \}$$
maybe in terms of the (partial) derivatives of (components of) $a$?
Here $n\ge1$, $K>0$, $\|\cdot\|$ stands for the Euclidean norm, and $"\cdot"$ denotes the dot product of vectors in $\mathbb{R}^n$.
We also assume that $a$ is e.g. Lipschitz continuous so that it has partial derivatives a.e.
For example for $n=1$, $A=\{a:\mathbb{R}\to\mathbb{R}\mid\ a'\ge K,\ \rm{a.e.\ in}\ \mathbb{R}\}$.