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stochastic control representation

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Exponential convergence for a convexifyingequation
Guillaume Carlier, Alfred Galichon
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 18 / Issue 3 / July 2012

Published online by Cambridge University Press:

22 July 2011, pp. 611-620

Print publication:

July 2012
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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.