Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem∗
Dip. di Matematica Pura ed Applicata, Università di
Padova, via Trieste
Revised: 14 November 2011
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.
Mathematics Subject Classification: 35B25 / 35B30 / 35J60 / 35K55 / 49L25 / 49N70
Key words: Continuous dependence estimates / parabolic Hamilton-Jacobi equations / viscosity solutions / ergodic problems / differential games / singular perturbations
© EDP Sciences, SMAI, 2012