Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 105 / 2 / b / i / Solution

The principal coefficients satisfy the positive uniformly elliptic operator condition if there is $\theta >0$, independent of $x$, such thatThe smooth coefficients on the compact closure also give a uniform upper bound $\sum a^{ij}{\xi }_i{\xi }_j\le \Theta |\xi {|}^2$. The first-order and zeroth-order coefficients do not enter uniform ellipticity.