Exponential convergence for a convexifying equation

Guillaume Carlier, Alfred Galichon

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)611-620
    Number of pages10
    JournalESAIM - Control, Optimisation and Calculus of Variations
    Volume18
    Issue number3
    DOIs
    StatePublished - Jul 1 2012

    Keywords

    • Convex envelope
    • Nonautonomous gradient flows
    • Stochastic control representation
    • Viscosity solutions

    ASJC Scopus subject areas

    • Control and Systems Engineering
    • Control and Optimization
    • Computational Mathematics

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