Strict ellipticity (${\xi }^{T}A(x)\xi >0(\xi \ne 0)$)

For a real symmetric matrix field $A$, strict ellipticity means that $A(x)$ is a positive-definite matrix at every point. Continuity makes its smallest eigenvalue positive uniformly on each compact subset of the domain. A uniform positive lower bound on the entire domain is the stronger uniform ellipticity condition. Some conventions include a finite uniform upper bound in the latter term, while others state coefficient boundedness separately.