Uniformly convex variational integrand
= Uniformly convex variational integrand
{title2=$F_{pp}(x,p)\geq\lambda I$}
A gradient integrand is uniformly convex in this elliptic variational sense when its <Hessian matrix> in the gradient variables has a common positive lower bound. Then $(F_p(x,p)-F_p(x,q))\cdot(p-q)\geq\lambda|p-q|^2$. Averaging $F_{pp}$ along a line segment in gradient space preserves the same lower bound.