$\Gamma$-convergence for functionals depending on vector fields. II. Convergence of minimizers

Abstract

Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots ,X_m(x))$ on ${\mathbb{R}}^n$, $m\le n$, we study integral functionals depending on $X$. Using the results in \cite{MPSC1}, 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 to prove a $H$-compactness theorem for linear differential operators of the second order depending on $X$.

References in corpus (3)

• $\Gamma$-convergence for functionals depending on vector fields. I. Integral representation and compactness
• Integral representation of local left--invariant functionals in Carnot groups
• $H$-convergence for equations depending on monotone operators in Carnot groups

Cited by in corpus (2)

• $G$-convergence of elliptic and parabolic operators depending on vector fields
• $H$-compactness for nonlocal linear operators in fractional divergence form