Exponential convergence for a convexifying equation and a non-autonomous gradient flow for global minimization

Details Exponential convergence for a convexifying equation and a non-autonomous gradient flow for global minimization Exponential convergence for a convexifying equation and a non-autonomous gradient flow for global minimization

2010-03-09

arxiv.org/abs/1003.1928v2

Mathematics

Analysis of PDEs

Scientific paper

We consider an evolution equation similar to that introduced by Vese 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.

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