Calculus of Variations and Geometric Measure Theory

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 05 Nov 2022

[BibTeX]

Published Paper

Inserted: 26 apr 2021
Last Updated: 5 nov 2022

Journal: SIAM J. Math. Anal.
Volume: 54
Number: 6
Pages: 5761-5791
Year: 2022
Doi: 10.1137/21M1432466

ArXiv: 2104.12892 PDF
Links: Link

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 $X$.

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


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