I will present a $\Gamma$-convergence for degenerate integral functionals related to homogenisation problems in the Heisenberg group. In our case, both the rescaling and the notion of invariance or periodicity are chosen in a way motivated by the geometry of the Heisenberg group. Without using special geometric features, these functionals would be neither coercive nor periodic, so classic results do not apply. All the results apply to the more general case of Carnot groups. Joint with Nicolas Dirr, Paola Mannucci and Claudio Marchi.
- Partial Differential Equations Seminar