MAXIMIZATION AND MINIMIZATION PROBLEMS RELATED TO A $p$-LAPLACIAN EQUATION ON A MULTIPLY CONNECTED DOMAIN

Abstract

In this paper we investigate maximization and minimization problems related to a $p$-Laplacian equation on a multiply connected domain in $\mathbb{R}^2$, where the admissible set is a rearrangement class of a fixed function. We prove existence and representation of the maximizers and existence, uniqueness and representation of the minimizer.