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Continuous dependence estimates for the ergodic problem ofBellman-Isaacs operators via the parabolic Cauchy problem∗

Published online by Cambridge University Press:  16 January 2012

Claudio Marchi
Claudio Marchi*
Affiliation:
Dip. di Matematica Pura ed Applicata, Università di Padova, via Trieste 63, 35121 Padova, Italy. marchi@math.unipd.it

Abstract

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This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacsoperators. We establish such an estimate for the parabolic Cauchy problem in the wholespace  [0, +∞) × ℝn and, under some periodicity and eitherellipticity or controllability assumptions, we deduce a similar estimate for the ergodicconstant associated to the operator. An interesting byproduct of the latter result will bethe local uniform convergence for some classes of singular perturbation problems.

Keywords

Continuous dependence estimatesparabolic Hamilton-Jacobi equationsviscosity solutionsergodic problemsdifferential gamessingular perturbations

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012, pp. 954 - 968
Copyright
© EDP Sciences, SMAI, 2012

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