On closure of the class of homeomorphisms with integrable distortion and the minimization of functionals

It is known that the limit of a sequence of (quasi)conformal mappings is either a constant or a (quasi)conformal mapping. In this paper, we prove that in the case of Heisenberg-type Carnot groups, a similar property is valid for mappings that are quasiconformal in the mean, i.e., for homeomorphisms with finite distortion and a distortion function integrable to an appropriate degree. This result is applied to solving model problems of nonlinear elasticity theory on Carnot groups.