# $\Gamma$- convergence and homogenisation for a class of degenerate functionals

## TL;DR

This paper studies the $ ext{Gamma}$-convergence of degenerate integral functionals in the Heisenberg and Carnot groups, addressing challenges posed by their geometric structure to establish homogenisation results.

## Contribution

It introduces a novel approach to $ ext{Gamma}$-convergence for degenerate functionals respecting the geometry of Heisenberg and Carnot groups, overcoming limitations of classic methods.

## Key findings

- Established $ ext{Gamma}$-convergence results for degenerate functionals
- Extended homogenisation techniques to Heisenberg and Carnot groups
- Addressed non-coercivity and non-periodicity issues in the geometric setting

## Abstract

This paper is on $\Gamma$-convergence for degenerate integral functionals related to homogenisation problems in the Heisenberg group. Here 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.