Symmetry of optimal solution when domain is symmetric

Zivari-Rezapour, Mohsen; Jalalvand, Mehdi

doi:10.22055/jamm.2016.12305

Symmetry of optimal solution when domain is symmetric

Document Type : Original Paper

Authors

Mohsen Zivari-Rezapour

Mehdi Jalalvand

Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

10.22055/jamm.2016.12305

Abstract

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.

Keywords

Laplacian equation

maximization problem

optimal solution

Rearrangement

symmetry

uniqueness

Subjects

Differential Equations

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