Lucio Cadeddu, Maria Antonietta Farina, Giovanni Porru
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 results,
and present some features of the optimizers. In special cases, we
prove results of symmetry and results of symmetry breaking for the
minimizer.
Submitted November 26, 2013. Published July 5, 2014.
Math Subject Classifications: 47A75, 35J25, 35Q92, 49J20, 49K20.
Key Words: Principal eigenvalue; rearrangements; minimization;
maximization, symmetry breaking; population dynamics.
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Lucio Cadeddu Dipartimento di Matematica e Informatica, Univ. di Cagliari Via Ospedale 72, 09124 Cagliari, Italy email: cadeddu@unica.it |
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Maria Antonietta Farina Dipartimento di Matematica e Informatica, Univ. di Cagliari Via Ospedale 72, 09124 Cagliari, Italy email: mafarina@unica.it |
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Giovanni Porru Dipartimento di Matematica e Informatica, Univ. di Cagliari Via Ospedale 72, 09124 Cagliari, Italy email: porru@unica.it |
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