Calculus of Variations and Geometric Measure Theory

P. Tilli - D. Zucco

Spectral partitions for Sturm-Liouville problems

created by zucco on 17 Jul 2018
modified on 14 Dec 2018


Accepted Paper

Inserted: 17 jul 2018
Last Updated: 14 dec 2018

Journal: Proc. Roy. Soc. Edinburgh Sect. A
Year: 2018

ArXiv: 1807.05973 PDF


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