Optimization of the first eigenvalue of equations with indefinite weights

Cosner, C;CUCCU, FABRIZIO;Porru, G.

2013-01-01

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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.