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Exponential convergence for a convexifyingequation

Published online by Cambridge University Press:  22 July 2011

Guillaume Carlier and
Alfred Galichon
Guillaume Carlier
Affiliation:
CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France. carlier@ceremade.dauphine.fr
Alfred Galichon
Affiliation:
Département d’Économie, UMR CNRS 7176, École polytechnique, 91128 Palaiseau Cedex, France; alfred.galichon@polytechnique.edu

Abstract

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

Keywords

Convex envelopeviscosity solutionsstochastic control representationnonautonomous gradient flows

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 3 , July 2012, pp. 611 - 620
Copyright
© EDP Sciences, SMAI, 2011

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