Density estimates for a fluid jet model in the Heisenberg group

In the Heisenberg group setting, we consider a fluid jet functional and we prove some density estimates for local minima. In particular, for large r, the measure of the minimal jet in balls of radius r centered at the jet is of the order of rQ−1, while the measure of the exterior medium is of the order of rQ, where Q=2(n+1) is the homogeneous dimension. Also, we obtain that , in a suitable weak sense, at the free boundary ξ∈∂{|u|<1}.