Spectral partitions for Sturm–Liouville problems
Copyright policy )Spectral partitions for Sturm–Liouville problems
AbstractWe 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.
Methods involving semicontinuity and convergence; relaxation, Sturm-Liouville theory, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, Optimization and Control (math.OC), Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, Classical Analysis and ODEs (math.CA), FOS: Mathematics, optimal partitions, Sturm-Liouville eigenvalue, \(\Gamma\)-convergence, optimization, Mathematics - Optimization and Control, Variational methods for eigenvalues of operators, Analysis of PDEs (math.AP)
Methods involving semicontinuity and convergence; relaxation, Sturm-Liouville theory, Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, Optimization and Control (math.OC), Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, Classical Analysis and ODEs (math.CA), FOS: Mathematics, optimal partitions, Sturm-Liouville eigenvalue, \(\Gamma\)-convergence, optimization, Mathematics - Optimization and Control, Variational methods for eigenvalues of operators, Analysis of PDEs (math.AP)
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