### Abstract

We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573-1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.

Original language | English (US) |
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Pages (from-to) | 611-620 |

Number of pages | 10 |

Journal | ESAIM - Control, Optimisation and Calculus of Variations |

Volume | 18 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 2012 |

### Keywords

- Convex envelope
- Nonautonomous gradient flows
- Stochastic control representation
- Viscosity solutions

### ASJC Scopus subject areas

- Control and Systems Engineering
- Control and Optimization
- Computational Mathematics

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## Cite this

Carlier, G., & Galichon, A. (2012). Exponential convergence for a convexifying equation.

*ESAIM - Control, Optimisation and Calculus of Variations*,*18*(3), 611-620. https://doi.org/10.1051/cocv/2011163