$\Gamma$-convergence for functionals depending on vector fields. I. Integral representation and compactness

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 functionals depending on $X$. We prove an integral representation for local functionals with respect to $X$ and a result of $\Gamma$-compactness for a class of integral functionals depending on $X$.

References in corpus (1)

• Integral representation of local left--invariant functionals in Carnot groups

Cited by in corpus (4)

• $\Gamma$-convergence for functionals depending on vector fields. II. Convergence of minimizers
• $H$-convergence for equations depending on monotone operators in Carnot groups
• $G$-convergence of elliptic and parabolic operators depending on vector fields
• $H$-compactness for nonlocal linear operators in fractional divergence form