This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators. We establish such an estimate for the parabolic Cauchy problem in the whole space [0, +∞) × ℝn and, under some periodicity and either ellipticity or controllability assumptions, we deduce a similar estimate for the ergodic constant associated to the operator. An interesting byproduct of the latter result will be the local uniform convergence for some classes of singular perturbation problems.
Mots clés : continuous dependence estimates, parabolic Hamilton-Jacobi equations, viscosity solutions, ergodic problems, differential games, singular perturbations
@article{COCV_2012__18_4_954_0,
author = {Marchi, Claudio},
title = {Continuous dependence estimates for the ergodic problem of {Bellman-Isaacs} operators via the parabolic {Cauchy} problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {954--968},
publisher = {EDP-Sciences},
volume = {18},
number = {4},
year = {2012},
doi = {10.1051/cocv/2011203},
mrnumber = {3019467},
zbl = {1262.35030},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2011203/}
}
TY - JOUR AU - Marchi, Claudio TI - Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 954 EP - 968 VL - 18 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2011203/ DO - 10.1051/cocv/2011203 LA - en ID - COCV_2012__18_4_954_0 ER -
%0 Journal Article %A Marchi, Claudio %T Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 954-968 %V 18 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2011203/ %R 10.1051/cocv/2011203 %G en %F COCV_2012__18_4_954_0
Marchi, Claudio. Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 954-968. doi : 10.1051/cocv/2011203. http://www.numdam.org/articles/10.1051/cocv/2011203/
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