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.
Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations
MARCHI, CLAUDIO
2012
Abstract
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.File in questo prodotto:
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