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 Holder 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. (C) 2012 Elsevier Ltd. All rights reserved.
Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations / Camilli, Fabio; Claudio, Marchi. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 75:13(2012), pp. 5103-5118. [10.1016/j.na.2012.04.026]
Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations
CAMILLI, FABIO;
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 Holder 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. (C) 2012 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.