Optimisation of Robin Laplacian eigenvalue with indefinite weight in spherical shell

2024/10/04 by Baruch Schneider, Diana Schneiderová, Schneider, Baruch +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2410.03498

openalex publication_date 2024/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with an optimisation problem of Robin Laplacian eigenvalue with respect to an indefinite weight, which is formulated as a shape optimisation problem thanks to the known bang-bang distribution of the optimal weight function. The minimisation of the principal eigenvalue of the problem in a spherical shell of an arbitrary dimension is fully solved.

Cited by

• One-dimensional optimisation of indefinite-weight principal eigenvalues with asymmetric Robin parameters and a Schrödinger-type perturbation

Related

• One-dimensional optimisation of indefinite-weight principal eigenvalues with asymmetric Robin parameters and a Schrödinger-type perturbation
• Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions
• On the optimization of the Robin eigenvalues in some classes of polygons
• Some Remarks on Robin-Laplacian Eigenvalues
• Asymptotic spherical shapes in some spectral optimization problems