Geodesic
Exponential convergence for a convexifying equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 611-620 Cet article a éte moissonné depuis la source Numdam

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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 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
Keywords: convex envelope, viscosity solutions, stochastic control representation, nonautonomous gradient flows 
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     author = {Carlier, Guillaume and Galichon, Alfred},
     title = {Exponential convergence for a convexifying equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {611--620},
     year = {2012},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {3},
     doi = {10.1051/cocv/2011163},
     mrnumber = {3041657},
     zbl = {1255.35041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011163/}
}
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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

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