Multiscale nonconvex relaxation and application to thin films



Jean-François Babadjian
L.P.M.T.M.
Université Paris Nord
93430, Villetaneuse, France
jfb@galilee.univ-paris13.fr



Margarida Baía
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA
mbaia@andrew.cmu.edu



Abstract: $ \Gamma$-convergence techniques are used to give a characterization of the behavior of a family of heterogeneous multiple scale integral functionals. Periodicity, standard growth conditions and nonconvexity are assumed whereas a stronger uniform continuity with respect to the macroscopic variable, normally required in the existing literature, is avoided. An application to dimension reduction problems in reiterated homogenization of thin films is presented.

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