Exponential convergence for a convexifying equation and a non-autonomous gradient ow for global minimization
FR : Édition Diffusion Presse Sciences
611 - 620 p.
We consider an evolution equation similar to that introduced by Vese in  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. We then introduce a non-autonomous gradient flow and prove that its trajectories all converge to minimizers of the convex envelope.