Asymptotic spherical shapes in some spectral optimization problems

Link identifier #identifier__6704-1Link identifier #identifier__187924-2
Mercoledì 11 dicembre, alle ore 15.00, il Dipartimento di Matematica e Fisica ospiterà il Seminario del prof. Gianmaria Verzini del Politecnico di Milano, presso l'aula 311 della palazzina C di Largo San Leonardo Murialdo 1. 


Abstract: We study the positive principal eigenvalue of a weighted problem associated with the Neumann Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. When trying to minimize such eigenvalue with respect to the weight, one is lead to consider a shape optimization problem, which is known to admit spherical optimal shapes only in very specific cases. We investigate whether spherical shapes can be recovered in general situations, in some singular perturbation limit. We also consider a related problem, where the diffusion is triggered by a fractional s-Laplacian, and the optimization is performed with respect to the fractional order s ∈ (0,1]. These are joint works with Dario Mazzoleni and Benedetta Pellacci.