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EnglishWe investigate minimization and maximization of the principal eigenvalue of the Laplacian under mixed boundary conditions in case the weight has indefinite sign and varies in a class of rearrangements. Biologically, these 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. We prove existence and uniqueness re- sults, and present some features of the optimizers. In special cases, we prove results of symmetry and results of symmetry breaking for the minimizer.
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| Titolo: | Optimization of the principal eigenvalue under mixed boundary conditions | |
| Autori: | ||
| Data di pubblicazione: | 2014 | |
| Rivista: | ||
| Abstract: | We investigate minimization and maximization of the principal eigenvalue of the Laplacian under mixed boundary conditions in case the weight has indefinite sign and varies in a class of rearrangements. Biologically, these 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. We prove existence and uniqueness re- sults, and present some features of the optimizers. In special cases, we prove results of symmetry and results of symmetry breaking for the minimizer. | |
| Handle: | http://hdl.handle.net/11584/101035 | |
| Tipologia: | 1.1 Articolo in rivista |
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