### 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) |
---|---|

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 2012 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*ESAIM - Control, Optimisation and Calculus of Variations*,

*18*(3), 611-620. https://doi.org/10.1051/cocv/2011163

**Exponential convergence for a convexifying equation.** / Carlier, Guillaume; Galichon, Alfred.

Research output: Contribution to journal › Article

*ESAIM - Control, Optimisation and Calculus of Variations*, vol. 18, no. 3, pp. 611-620. https://doi.org/10.1051/cocv/2011163

}

TY - JOUR

T1 - Exponential convergence for a convexifying equation

AU - Carlier, Guillaume

AU - Galichon, Alfred

PY - 2012/7

Y1 - 2012/7

N2 - 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.

AB - 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.

KW - Convex envelope

KW - Nonautonomous gradient flows

KW - Stochastic control representation

KW - Viscosity solutions

UR - http://www.scopus.com/inward/record.url?scp=84871489416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871489416&partnerID=8YFLogxK

U2 - 10.1051/cocv/2011163

DO - 10.1051/cocv/2011163

M3 - Article

VL - 18

SP - 611

EP - 620

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

SN - 1292-8119

IS - 3

ER -