Regularity and optimal design results for elastic membranes
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Submission date: 03. Jul. 1998
MSC-Numbers: 35J20, 35E99, 35M10, 49J45, 49N60, 49Q20, 73C50, 73M25
Keywords and phrases: gamma-limit, relaxation, thin films, image segmentation, morrey spaces, bounded variation
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The effective energy of a mixture of two elastic materials in a thin film is characterized using Gamma-limit techniques. For cylindrical shaped inclusions it is shown that 3D-2D asymptotics and optimal design commute from a variational viewpoint. Regularity of local minimizers for the resulting design is addressed.