Applied Mathematics & Optimization

, Volume 72, Issue 3, pp 523–547

Homogenization of Functionals with Linear Growth in the Context of \(\mathcal A\)-quasiconvexity


DOI: 10.1007/s00245-015-9289-1

Cite this article as:
Matias, J., Morandotti, M. & Santos, P.M. Appl Math Optim (2015) 72: 523. doi:10.1007/s00245-015-9289-1


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.


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

Mathematics Subject Classification

Primary 35B27 Secondary 49J40 49K20 35E99 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

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

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