Optimization of the first eigenvalue of equations with indefinite weights

Chris Cosner; Fabrizio Cuccu; Giovanni Porru

doi:10.1515/ans-2013-0105

Optimization of the first eigenvalue of equations with indefinite weights

Chris Cosner, Fabrizio Cuccu, Giovanni Porru

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We investigate minimization and maximization of the principal eigenvalue of the Laplacian under Dirichlet boundary conditions in case the weight has indefinite sign and varies in a class of rearrangements. Biologically, such optimization problems are motivated by the question of determining the most convenient spatial arrangement of favorable and unfavorable resources for a species to survive or to decline. The question may have practical importance in the context of reserve design or pest control.

Original language	English (US)
Pages (from-to)	79-95
Number of pages	17
Journal	Advanced Nonlinear Studies
Volume	13
Issue number	1
DOIs	https://doi.org/10.1515/ans-2013-0105
State	Published - Feb 2013

Keywords

Eigenvalue problems
Optimization
Population dynamics
Rearrangements
Spatial heterogeneity

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematics(all)

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AU - Porru, Giovanni

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AB - We investigate minimization and maximization of the principal eigenvalue of the Laplacian under Dirichlet boundary conditions in case the weight has indefinite sign and varies in a class of rearrangements. Biologically, such optimization problems are motivated by the question of determining the most convenient spatial arrangement of favorable and unfavorable resources for a species to survive or to decline. The question may have practical importance in the context of reserve design or pest control.

KW - Eigenvalue problems

KW - Optimization

KW - Population dynamics

KW - Rearrangements

KW - Spatial heterogeneity

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Optimization of the first eigenvalue of equations with indefinite weights

Abstract

Keywords

ASJC Scopus subject areas

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