We carry on our study of the connection between two shape optimization problems with spectral cost. On the one hand, we consider the optimal design problem for the survival threshold of a population living in a heterogenous habitat; this problem arises when searching for the optimal shape and location of a shelter zone in order to prevent extinction of the species. On the other hand, we deal with the spectral drop problem, which consists in minimizing a mixed Dirichlet-Neumann eigenvalue in a box. In a previous paper we proved that the latter one can be obtained as a singular perturbation of the former, when the region outside the refuge is more and more hostile. In this paper we sharpen our analysis in case the box is a planar polygon, providing quantitative estimates of the optimal level convergence, as well as of the involved eigenvalues.
|Titolo della pubblicazione ospite||2018 MATRIX ANNALS|
|Stato di pubblicazione||Pubblicato - 2019|
|Evento||MATRIX 2018 - Melbourne (Australia)|
Durata: 5 nov 2018 → 16 nov 2018
|Periodo||5/11/18 → 16/11/18|
- Singular limits, survival threshold, mixed Neumann-Dirichlet boundary conditions