Nondivergence-form elliptic operator
= Nondivergence-form elliptic operator
{title2=$Lu=a^{ij}D_{ij}u+b^iD_i u+cu$}
A <nondivergence-form elliptic operator> applies its principal coefficients directly to the <Hessian matrix>: $Lu=a^{ij}D_{ij}u+b^iD_i u+cu$. Only the symmetric part of $a$ contributes to the second-derivative term. <Uniform ellipticity> bounds its <quadratic form> below by $\lambda|\xi|^2$ with a constant $\lambda>0$ independent of position.