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

TL;DR

This paper extends continuous dependence estimates to quasi-monotone systems of fully nonlinear second-order parabolic equations, providing new regularity and homogenization results with practical convergence rates.

Contribution

It introduces extended continuous dependence estimates for such systems and applies these to establish homogenization results and convergence rates.

Findings

Hölder estimate for bounded solutions

Rate of convergence for vanishing viscosity approximation

Periodic homogenization results for quasi-monotone systems

Abstract

Aim of this paper is to extend the continuous dependence estimates proved in \cite{JK1} to quasi-monotone systems of fully nonlinear second-order parabolic equations. As by-product of these estimates, we get an H\"older 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.