  This is a simplification of our prior work on the existence theory for the
Rosseland-type equations.
  Inspired by the Rosseland equation in the conduction-radiation coupled heat
transfer, we use the locally arbitrary growth conditions instead of the common
global restricted growth conditions.
  In the Lebesgue square integrable space, the solution to the linear elliptic
equation depends continuously on the coefficients matrix. This is a simple
version of the maximal regularity. There exists a fixed point for the
linearized map (compact and continuous) in a closed convex set. We also
consider the Galerkin method.
