Optimization of the principal eigenvalue under mixed boundary conditions
CADEDDU, LUCIO;FARINA, MARIA ANTONIETTA
2014-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.