Minimization of the first eigenvalue for the Lamé system
Abstract
We study the minimization, under a volume constraint, of the first eigenvalue of the Lamé system in R N .We first prove the existence of an optimal domain in the class of quasi-open sets and show that, in the physically relevant dimensions N = 2 and N = 3, every optimal domain is open.We then derive first and second-order optimality conditions.In dimension two, these conditions imply that the disk is not optimal when the Poisson ratio is below a certain threshold, whereas it is a local minimizer above this threshold.We further prove that the disk is not optimal for all Poisson ratios ν satisfying ν ≤ 0.4.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Quantum chaos and dynamical systems
Mathematical and Theoretical Epidemiology and Ecology Models
Publication details
- Journal / source
- ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- Publisher
- Scuola Normale Superiore - Edizioni della Normale
- Pages
- 53–53
- Publication date
- 26 June 2026
- Language
- EN