Optimization of the principal eigenvalue under mixed boundary conditions

CADEDDU, LUCIO;Porru G;FARINA, MARIA ANTONIETTA

2014-01-01

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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.