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

Homogenization of Functionals with Linear Growth in the Context of $$\mathcal A$$ A -quasiconvexity This work deals with the homogenization of functionals with linear growth in the context of $$\mathcal A$$ 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 $$\mathcal A$$ A -free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

, Volume 72 (3) – Dec 1, 2015
25 pages

/lp/springer_journal/homogenization-of-functionals-with-linear-growth-in-the-context-of-umWkuD7PyB
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-015-9289-1
Publisher site
See Article on Publisher Site

### Abstract

This work deals with the homogenization of functionals with linear growth in the context of $$\mathcal A$$ 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 $$\mathcal A$$ A -free condition plays a crucial role. This result extends some previous work to the linear case, thus allowing for concentration effects.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 1, 2015

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