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

2011/09/19 by Fabio Camilli, Camilli, Fabio, Claudio Marchi +1 · 1 citation
Computer Science · Mathematics · Engineering · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.1109.4136

Abstract

Aim of this paper is to extend the continuous dependence estimates proved in\n citeJK1 to quasi-monotone systems of fully nonlinear second-order parabolic\nequations. As by-product of these estimates, we get an H "older estimate for\nbounded solutions of systems and a rate of convergence estimate for the\nvanishing viscosity approximation. In the second part of the paper we employ\nsimilar techniques to study the periodic homogenization of quasi-monotone\nsystems of fully nonlinear second-order uniformly parabolic equations. Finally,\nsome examples are discussed.\n

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