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OPTIMAL PARTITIONS FOR EIGENVALUES
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DOI：10.1137/090747087.png)
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Abstract
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We introduce a new numerical method for approximating partitions of a domain minimizing the sum of Dirichlet-Laplacian eigenvalues of any order. First we prove the equivalence of the original problem and a relaxed formulation based on measures. Using this result, we build a numerical algorithm to approximate optimal configurations. We describe numerical experiments aimed at studying the asymptotic behavior of optimal partitions with large numbers of cells.
Keywords:
gamma-convergence
shape analysis
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