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Abstract: We consider an evolution equation similar to that introduced by Vese andwhose solution converges in large time to the convex envelope of the initialdatum. We give a stochastic control representation for the solution from whichwe deduce, under quite general assumptions that the convergence in theLipschitz norm is in fact exponential in time. We then introduce anon-autonomous gradient flow and prove that its trajectories all converge tominimizers of the convex envelope.



Author: Guillaume Carlier, Alfred Galichon

Source: https://arxiv.org/







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