Maximization and minimization problems related to an equation with the p-Laplacian

N. Amiri () and M. Zivari-Rezapour ()
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N. Amiri: Shahid Chamran University of Ahvaz
M. Zivari-Rezapour: Shahid Chamran University of Ahvaz

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 2, 777-788

Abstract: Abstract In this paper, we investigate two optimization problems related to a quasilinear elliptic equation with p-Laplacian, logistic-type growth rate function such that the admissible set is a class of rearrangements of a fixed function. Under some suitable assumptions, we prove existence and representation of the maximizers and existence, uniqueness and representation of the minimizer. Also, when the domain of the equation is a ball, we show that the maximizer is unique and symmetric.

Keywords: Existence; maximization; minimization; rearrangement; symmetric; uniqueness; 35J20; 49J20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0430-8

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