*Published Paper*

**Inserted:** 11 apr 2019

**Last Updated:** 6 jun 2020

**Journal:** J. Math. Pures Appl.

**Volume:** 139

**Pages:** 109-142

**Year:** 2020

**Doi:** 10.1016/j.matpur.2020.05.003

**Abstract:**

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 $\Gamma$-compactness for a class of integral functionals depending on $X$.

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