$\mathrm{\Gamma }$-Compactness of Some Classes of Integral Functionals Depending on Vector Fields

In this paper we achieve some $\mathrm{\Gamma }$-compactness results for suitable classes of integral functionals depending on a given family of Lipschitz vector fields, with respect to both the strong $L^p-$topology and the strong $W_X^{1,p}-$topology.