Exponential convergence for a convexifying equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 611-620.

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.

DOI : 10.1051/cocv/2011163
Classification : 35B40, 49L20, 93E20
Mots clés : convex envelope, viscosity solutions, stochastic control representation, nonautonomous gradient flows
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     title = {Exponential convergence for a convexifying equation},
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     publisher = {EDP-Sciences},
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Carlier, Guillaume; Galichon, Alfred. Exponential convergence for a convexifying equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 611-620. doi : 10.1051/cocv/2011163. http://www.numdam.org/articles/10.1051/cocv/2011163/

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