  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.
