Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations

The aim of this paper is to extend the continuous dependence estimates proved by Jakobsen and Karlsen (2002) [3] to quasi-monotone systems of fully nonlinear second order parabolic equations. As a by-product of these estimates, we get an Hölder estimate for bounded solutions of systems and a rate of convergence estimate for the vanishing viscosity approximation.In the second part of the paper we employ similar techniques to study the periodic homogenization of quasi-monotone systems of fully nonlinear second order uniformly parabolic equations. Finally, some examples are discussed.