| Issue |
ESAIM: COCV
Volume 18, Number 3, July-September 2012
|
|
|---|---|---|
| Page(s) | 611 - 620 | |
| DOI | https://doi.org/10.1051/cocv/2011163 | |
| Published online | 22 July 2011 | |
Exponential convergence for a convexifying equation
1
CEREMADE, UMR CNRS 7534, Université Paris IX
Dauphine, Pl. de Lattre de
Tassigny, 75775
Paris Cedex 16,
France
carlier@ceremade.dauphine.fr
2
Département d’Économie, UMR CNRS 7176,
École polytechnique,
91128
Palaiseau Cedex,
France
alfred.galichon@polytechnique.edu
Received:
20
November
2010
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.
Mathematics Subject Classification: 35B40 / 49L20 / 93E20
Key words: Convex envelope / viscosity solutions / stochastic control representation / nonautonomous gradient flows
© EDP Sciences, SMAI, 2011
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