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.

Mazzoleni, D. C. S., Pellacci, B., Verzini, G., Quantitative analysis of a singularly perturbed shape optimization problem in a polygon, Paper, in 2018 MATRIX ANNALS, (Melbourne (Australia), 05-16 November 2018), Springer International Publishing, New York 2019: N/A-N/A [http://hdl.handle.net/10807/142606]

Quantitative analysis of a singularly perturbed shape optimization problem in a polygon

Mazzoleni, Dario Cesare Severo;
2019

Abstract

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.
2019
Inglese
2018 MATRIX ANNALS
MATRIX 2018
Melbourne (Australia)
Paper
5-nov-2018
16-nov-2018
Springer International Publishing
Mazzoleni, D. C. S., Pellacci, B., Verzini, G., Quantitative analysis of a singularly perturbed shape optimization problem in a polygon, Paper, in 2018 MATRIX ANNALS, (Melbourne (Australia), 05-16 November 2018), Springer International Publishing, New York 2019: N/A-N/A [http://hdl.handle.net/10807/142606]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/142606
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact