Speaker
Prof.
Riccardo Scala
(Università di Siena)
Description
We discuss the relaxation on $L^1$ of polyconvex functions with linear growth, and recall some old and new results. As prototype of this class of energies, the analysis of the area functional leads to the main example of nonlocality and non-subadditivity, actually confirming a conjecture by De Giorgi (proved by Acerbi and Dal Maso). We discuss what has been recently done to understand the behaviour of this kind of energies and we show how the situation is completely different when one considers relaxation under stronger topologies than $L^1$, as for instance the strict convergence in BV.
