Abstract

We study the problem of minimizing the first eigenvalue of the p-Laplacian operator for a two-phase material in a bounded open domain Omega subset of R-N, N >= 2 assuming that the amount of the best material is limited. We provide a relaxed formulation of the problem and prove some smoothness results for these solutions. As a consequence we show that if Omega is of class C-1,C-1, simply connected with connected boundary, then the unrelaxed problem has a solution if and only if Omega is a ball. We also provide an algorithm to approximate the solutions of the relaxed problem and perform some numerical simulations. (C) 2021 Elsevier B.V. All rights reserved.