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arXiv · 1904.06454

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

Alberto Maione·Andrea Pinamonti·Francesco Serra Cassano
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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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Alberto Maione, Andrea Pinamonti, Francesco Serra Cassano. 2019-04-13. $\Gamma$-convergence for functionals depending on vector fields. I. Integral representation and compactness. https://doi.org/10.1016/j.matpur.2020.05.003

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