On nonlocal perimeter and curvature for measurable sets

par Julian Toledo (Université de Valence (Espagne))

vendredi 4 mars 2016, 10:30 → 11:30 Europe/Paris

XLIM Salle X.203

We present a nonlocal perimeter associated with a nonnegative radial kernel J, compactly supported with \int_{R^n} J(z) dz = 1. The nonlocal perimeter of a measurable set E is given by the interactions of particles from the outside with particles from the inside (measured in terms on the kernel): P_J (E) = \int_E \int_{R^n \ E} J(x-y) dy dx. We will see that, when the kernel J is appropriately rescaled, the nonlocal perimeter converges to the classical local perimeter. We will introduce the concept of J-mean curvature on a point and the analogous to a Cheeger set in this nonlocal context. We will see the ralation between J-calibrability of a set and its J-mean curvature. Joint work with J.M. Mazon and J.D. Rossi.