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

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

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