Sturm-Liouville问题的谱剖分
Spectral partitions for Sturm-Liouville problems
摘要：
我们寻找最好的分区的单位间隔，最小化某些泛函定义的特征值的Sturm-Liouville问题。利用Γ-收敛理论，研究了当划分的区间数趋于无穷大时极小解的渐近分布。然后，我们讨论了几个例子，适合在我们的框架，如总和（正和负）权力的特征值和近似的热斯特姆-刘维算子的轨迹。
英文摘要：
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.
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