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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*
Affiliation:
Dip. di Matematica Pura ed Applicata, Università di Padova, via Trieste 63, 35121 Padova, Italy. [email protected]
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Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2012

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