Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem

Claudio Marchi

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 4, page 954-968
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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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 18.4 (2012): 954-968. <http://eudml.org/doc/272878>.

@article{Marchi2012,
abstract = {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.},
author = {Marchi, Claudio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {continuous dependence estimates; parabolic Hamilton-Jacobi equations; viscosity solutions; ergodic problems; differential games; singular perturbations},
language = {eng},
number = {4},
pages = {954-968},
publisher = {EDP-Sciences},
title = {Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem},
url = {http://eudml.org/doc/272878},
volume = {18},
year = {2012},
}

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
PB - EDP-Sciences
VL - 18
IS - 4
SP - 954
EP - 968
AB - 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.
LA - eng
KW - continuous dependence estimates; parabolic Hamilton-Jacobi equations; viscosity solutions; ergodic problems; differential games; singular perturbations
UR - http://eudml.org/doc/272878
ER -

References

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