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arXiv · 2104.12892

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

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 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 $X$.

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Alberto Maione, Andrea Pinamonti, Francesco Serra Cassano. 2021-04-26. $\Gamma$-convergence for functionals depending on vector fields. II. Convergence of minimizers. https://doi.org/10.1137/21m1432466

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