Francesca de Giovanni

arXiv2026

On the Effectless Cut Method for Laplacian Eigenvalues in any dimensions

In this paper, we study the optimization of the first Laplacian eigenvalue on axisymmetric doubly connected domains under positive Robin boundary conditions. Under additional geometric constraints, we prove that spherical shells maximize this eigenvalue. Our approach combines known isoperimetric inequalities for mixed Laplacian eigenvalues with a higher-dimensional extension of the effectless cut technique introduced by Hersch to study multiply connected membranes of given area fixed along their boundaries.

math.SP↗

arXiv2025

The asymptotic behavior of the first Robin eigenvalue with negative parameter as $p$ goes to $+\infty$

In this paper, we want to study the asymptotic behavior of the first $p$-Laplacian eigenvalue, with Robin boundary conditions, with negative boundary parameter. In particular, we prove that the limit of the eigenfunctions is a viscosity solution for the infinity Laplacian eigenvalue problem.

math.AP↗