Calculus of Variations and Geometric Measure Theory
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A. Maione - A. Pinamonti - F. Serra Cassano

Γ-convergence for functionals depending on vector fields. II. Convergence of minimizers

created by maione on 26 Apr 2021
modified on 28 Apr 2021


Submitted Paper

Inserted: 26 apr 2021
Last Updated: 28 apr 2021

Year: 2021

ArXiv: 2104.12892 PDF


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 $X$.

Keywords: Homogenization, Carnot groups, H-convergence, Γ-convergence, Vector fields


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