Exponential convergence for a convexifying equation

Galichon, Alfred; Carlier, Guillaume

Galichon, Alfred; Carlier, Guillaume (2012), Exponential convergence for a convexifying equation, ESAIM. COCV, 18, 3, p. 611-620. http://dx.doi.org/10.1051/cocv/2011163

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/1003.1928v2

Date

2012

Journal name

ESAIM. COCV

Volume

Number

Publisher

EDP Sciences

Pages

611-620

Abstract (EN)

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.

Subjects / Keywords

convex envelope; non-autonomous gradient ﬂows; stochastic control representation; viscosity solutions