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Journal of Convex Analysis 09 (2002), No. 2, 363--399
Copyright Heldermann Verlag 2002

Limits of Discrete Systems with Long-Range Interactions

Andrea Braides
S.I.S.S.A., via Beirut 4, 34013 Trieste, Italy

Maria Stella Gelli
S.I.S.S.A., via Beirut 4, 34013 Trieste, Italy

We prove that under some structure and decay hypotheses, limits of discrete systems with multi-neighbourhood interactions give rise to local energies with bulk and surface part, and that the limit energy densities can be recovered through a scaling and superposition procedure.

Keywords: Gamma-limit, thin films, homogenization.

MSC: 35E99, 49J45; 35M10, 73C50, 73M25

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