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

Fabio Camilli; Claudio Marchi

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arXiv · 1109.4136

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

Fabio Camilli·Claudio Marchi

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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 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.

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Fabio Camilli, Claudio Marchi. 2012-02-27. Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations. https://arxiv.org/abs/1109.4136

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