2012/06/07 by Antoine Levitt, Levitt, Antoine · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #math-ph #math.AP #math.MP #math.SP
paper · pdf · doi:10.48550/arxiv.1206.1473
arxiv created 2012/06/07 · openalex publication_date 2012/06/07 · arxiv updated 2012/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate numerically the optimal constants in Lieb-Thirring inequalities by studying the associated maximization problem. We use a monotonic fixed-point algorithm and a finite element discretization to obtain trial potentials which provide lower bounds on the optimal constants. We examine the one-dimensional and radial cases in detail. Our numerical results provide new lower bounds, insight into the behavior of the maximizers and confirm some existing conjectures. Based on our numerical results, we formulate a complete conjecture about the best constants for all possible values of the parameters.