Geodesic
Optimization of the principal eigenvalue under mixed boundary conditions
Electronic journal of differential equations, Tome 2014 (2014)
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 results, and present some features of the optimizers. In special cases, we prove results of symmetry and results of symmetry breaking for the minimizer.
Classification : 47A75, 35J25, 35Q92, 49J20, 49K20
Keywords: principal eigenvalue, rearrangements, minimization, maximization, symmetry breaking, population dynamics 
@article{EJDE_2014__2014__a111,
     author = {Cadeddu,  Lucio and Farina,  Maria Antonietta and Porru,  Giovanni},
     title = {Optimization of the principal eigenvalue under mixed boundary conditions},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1310.47024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a111/}
}
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%F EJDE_2014__2014__a111
Cadeddu,  Lucio; Farina,  Maria Antonietta; Porru,  Giovanni. Optimization of the principal eigenvalue under mixed boundary conditions. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a111/