# How to prove this equivalence?

Consider the general elliptic operator $$M=\sum_{i,j=1}^na_{ij}(x)\frac{\partial^2}{\partial x_i\partial x_j},$$ where $a_{ij}$ are continous functions. The function $u$ satisfies $$|Mu|\leq A(|\nabla u|+u+k) \ \ in \ \ \Omega,$$ if only if $$Mu=b_i(x)\frac{\partial}{\partial x_i}u+c(x)u=kf(x),$$ where $f$ and the coefficientes $b_i$, $c$ are measurable and are bounded in absolute value by a constant times $A$.

-