# Exponential convergence for a convexifying equation

Guillaume Carlier; Alfred Galichon

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

- Volume: 18, Issue: 3, page 611-620
- ISSN: 1292-8119

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topCarlier, Guillaume, and Galichon, Alfred. "Exponential convergence for a convexifying equation." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 611-620. <http://eudml.org/doc/277828>.

@article{Carlier2012,

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.
},

author = {Carlier, Guillaume, Galichon, Alfred},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Convex envelope; viscosity solutions; stochastic control representation; nonautonomous gradient flows; convex envelope},

language = {eng},

month = {11},

number = {3},

pages = {611-620},

publisher = {EDP Sciences},

title = {Exponential convergence for a convexifying equation},

url = {http://eudml.org/doc/277828},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Carlier, Guillaume

AU - Galichon, Alfred

TI - Exponential convergence for a convexifying equation

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/11//

PB - EDP Sciences

VL - 18

IS - 3

SP - 611

EP - 620

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.

LA - eng

KW - Convex envelope; viscosity solutions; stochastic control representation; nonautonomous gradient flows; convex envelope

UR - http://eudml.org/doc/277828

ER -

## References

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- L. Vese, A method to convexify functions via curve evolution. Comm. Partial Diff. Eq.24 (1999) 1573–1591.

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