Applied Mathematics & Optimization

, Volume 72, Issue 3, pp 523–547

# Homogenization of Functionals with Linear Growth in the Context of $$\mathcal A$$-quasiconvexity

• José Matias
• Marco Morandotti
• Pedro M. Santos
Article

## Abstract

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

$$\mathcal A$$-quasiconvexity Homogenization Representation of integral functionals Concentration effects

## Mathematics Subject Classification

Primary 35B27 Secondary 49J40 49K20 35E99

## Notes

### Acknowledgments

Partial support for this research was provided by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the Carnegie Mellon Portugal Program under Grant FCT-UTA_CMU/MAT/0005/2009 “Thin Structures, Homogenization, and Multiphase Problems”. The authors warmly thank the Centro de Análise Matemática, Geometria e Sistemas Dinâmicos (CAMGSD) at the Departamento de Matemática of the Instituto Superior Técnico, Universidade de Lisboa, where the research was carried out.

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## Authors and Affiliations

• José Matias
• 1
• Marco Morandotti
• 2
Email author
• Pedro M. Santos
• 1
1. 1.CAMGSD, Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal
2. 2.SISSA – International School for Advanced StudiesTriesteItaly