Spectral partitions for Sturm–Liouville problems

We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm–Liouville problems. Via Γ-convergence theory, we study the asymptotic distribution of the minimizers as the number of intervals of the partition tends to infinity. Then we...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2020-08, Vol.150 (4), p.2155-2173
Main Authors: Tilli, Paolo, Zucco, Davide
Format: Article
Language:English
Subjects:
Eigenvalues
Partitions (mathematics)
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Summary:We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm–Liouville problems. Via Γ-convergence theory, we study the asymptotic distribution of the minimizers as the number of intervals of the partition tends to infinity. Then we discuss several examples that fit in our framework, such as the sum of (positive and negative) powers of the eigenvalues and an approximation of the trace of the heat Sturm–Liouville operator.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2019.1