Inserted: 27 nov 2019
Last Updated: 27 nov 2019
Journal: Rend. Sem. Mat. Torino
The aim of this note is to review some recent results on a family of functionals penalizing oblique oscillations. These functionals naturally appeared in some variational problem related to pattern formation and are somewhat reminiscent of those introduced by Bourgain, Brezis and Mironescu to characterize Sobolev functions. We obtain both qualitative and quantitative results for functions of finite energy. It turns out that this problem naturally leads to the study of various differential inclusions and has connections with branched transportation models.