3D-2D asymptotic analysis of an optimal design problem for thin films
Irene Fonseca and Gilles Francfort
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Submission date: 09. Feb. 1998
published in: Journal für die reine und angewandte Mathematik, 505 (1998), p. 173-202
DOI number (of the published article): 10.1515/crll.1998.505.173
MSC-Numbers: 35E99, 35M10, 49J45, 73C50, 73M25
Keywords and phrases: gamma-limit, radon-nikodyn theorem, relaxation, thin films
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The Gamma-limit of a rescaled version of an optimal material distribution problem for a cylindrical two-phase elastic mixture in a thin three-dimensional domain is explicitly computed. Its limit is a two-dimensional optimal design problem on the cross-section of the thin domain; it involves optimal energy bounds on two-dimensional mixtures of a related two-phase bulk material. Thus, it is shown in essence that 3D-2D asymptotics and optimal design commute from a variational standpoint.