Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80886120160822Symmetry of optimal solution when domain is symmetricSymmetry of optimal solution when domain is symmetric81881230510.22055/jamm.2016.12305FAMohsenZivari-RezapourDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, IranMehdiJalalvandDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20160119In this paper, we consider a maximization problem related to a Laplacian equation with Dirichlet boundary conditions, where the admissible set is a rearrangement class of a non-negative function. When the domain of the equation is symmetric, under some suitable assumptions, we prove that the optimal solution of the maximization problem is symmetric and unique.In this paper, we consider a maximization problem related to a Laplacian equation with Dirichlet boundary conditions, where the admissible set is a rearrangement class of a non-negative function. When the domain of the equation is symmetric, under some suitable assumptions, we prove that the optimal solution of the maximization problem is symmetric and unique.https://jamm.scu.ac.ir/article_12305_ee94367473821db839d0f29c8415c33f.pdf