Design of a Composite Membrane with Patches |
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Authors: | Fabrizio Cuccu Behrouz Emamizadeh Giovanni Porru |
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Affiliation: | 1. Dipartimento di Matematica e Informatica, University of Cagliari, Cagliari, Italy 2. Department of Mathematics, The Petroleum Institute, Abu Dabi, United Arab Emirates
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Abstract: | This paper is concerned with minimization and maximization problems of eigenvalues. The principal eigenvalue of a differential operator is minimized or maximized over a set which is formed by intersecting a rearrangement class with an affine subspace of finite co-dimension. A solution represents an optimal design of a 2-dimensional composite membrane Ω, fixed at the boundary, built out of two different materials, where certain prescribed regions (patches) in Ω are occupied by both materials. We prove existence results, and present some features of optimal solutions. The special case of one patch is treated in detail. |
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