Optimization problems for eigenvalues of p-Laplace equations with indefinite weights

Abstract

This paper is concerned with minimization and maximization of the principal eigenvalue of \( p \)-Laplace equations depending on functions which belong to a class of rearrangements. In case of \( p = 2 \), this optimization problems are motivated by the question of determining the most convenient spatial arrangement of favorable and unfavorable resources for species to survive or to decline. We prove existence and uniqueness results, and present some features of optimizers. The radial case is discussed in detail.