$\Gamma$-Convergence for Functionals Depending on Vector Fields. II. Convergence of Minimizers
Alberto Maione, Andrea Pinamonti, Francesco Serra Cassano · SIAM Journal on Mathematical Analysis · 2022
Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study integral functionals depending on $X$. Using the results in [A. Maione, A. Pinamonti, and F. Serra Cassano, J. Math. Pures Appl. (9), 139 (2020), pp. 109--142], we study the convergence of minima, minimizers, and momenta of those functionals. Moreover, we apply these results to the periodic homogenization in Carnot groups and prove an $H$-compactness theorem for linear differential operators of the second order depending on $X$.