# Design of a Composite Membrane with Patches

Design of a Composite Membrane with Patches 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Design of a Composite Membrane with Patches

, Volume 62 (2) – Oct 1, 2010
16 pages

/lp/springer_journal/design-of-a-composite-membrane-with-patches-wRMtl4KkN5
Publisher
Springer-Verlag
Subject
Mathematics; Numerical and Computational Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-010-9098-5
Publisher site
See Article on Publisher Site

### 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.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2010

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