Calculus of Variations and Geometric Measure Theory

A. Maione - A. Pinamonti - F. Serra Cassano

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

created by pinamonti on 11 Apr 2019
modified by maione on 06 Jun 2020


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

ArXiv: 1904.06454 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 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 $X$.