Calculus of Variations and Geometric Measure Theory

J. Matias - M. Morandotti - P. M. Santos

Homogenization of functionals with linear growth in the context of $\mathcal{A}$-quasiconvexity

created by morandott on 02 Oct 2014
modified on 07 Feb 2017


Published Paper

Inserted: 2 oct 2014
Last Updated: 7 feb 2017

Journal: Applied Mathematics and Optimization
Volume: 72
Number: 3
Pages: 523-547
Year: 2015
Doi: 10.1007/s00245-015-9289-1

Preprint SISSA: 49-2014-MATE


This work deals with the homogenization of functionals with linear growth in the context of $\mathcal{A}$-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the coupling between homogenization and the $\mathcal{A}$-free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects.

Keywords: Homogenization, $\mathcal{A}$-quasiconvexity, representation of integral functionals, concentration effects