We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via Î"-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.

Spectral partitions for Sturm-Liouville problems

Zucco D.
2020-01-01

Abstract

We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via Î"-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.
2020
150
4
2155
2173
http://journals.cambridge.org
optimal partitions; optimization; Sturm-Liouville eigenvalue; Î"-convergence
Tilli P.; Zucco D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1728950
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