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Spectral partitions for Sturm–Liouville problems

Published online by Cambridge University Press:  22 May 2019

Paolo Tilli
Affiliation:
Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy (paolo.tilli@polito.it; davide.zucco@polito.it)
Davide Zucco
Affiliation:
Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy (paolo.tilli@polito.it; davide.zucco@polito.it)

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 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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2019

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