Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS
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6 décembre 2019: 1 événement

  • Séminaire d’Analyse Fonctionnelle

    Vendredi 6 décembre 13:45-15:00 - Panu Lahti - University of Augsburg

    A new Federer-type characterization of sets of finite perimeter

    Résumé : Federer’s characterization, which is a key result in the theory of functions of bounded variation (BV functions), states that a set is of finite perimeter (i.e. the set’s indicator function is a BV function) if and only if the n−1-dimensional Hausdorff measure of the set’s measure-theoretic boundary is finite. The measure-theoretic boundary consists of those points where both the set and its complement have positive upper density. I discuss recent work in which I show that the characterization remains true if the measure-theoretic boundary is replaced by a smaller boundary consisting of those points where the lower densities of both the set and its complement are at least a given positive constant.

    En savoir plus : Séminaire d’Analyse Fonctionnelle

6 décembre 2019: 1 événement