Symmetry of optimal solution when domain is symmetric

Document Type : Original Paper


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


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.


Main Subjects

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Volume 6, Issue 1
April 2016
Pages 81-88
  • Receive Date: 19 January 2016
  • Revise Date: 17 August 2016
  • Accept Date: 08 September 2016
  • First Publish Date: 08 September 2016