Geodesic
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

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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.

DOI : 10.1051/cocv/2011203
Classification : 35B25, 35B30, 35J60, 35K55, 49L25, 49N70
Keywords: 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://geodesic.mathdoc.fr/articles/10.1051/cocv/2011203/}
}
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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

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