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Publicly Available Published by De Gruyter March 10, 2016

Optimization of the First Eigenvalue of Equations with Indefinite Weights

Chris Cosner, Fabrizio Cuccu and Giovanni Porru

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.

Published Online: 2016-03-10
Published in Print: 2013-02-01

© 2016 by Advanced Nonlinear Studies, Inc.

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