Symmetry of optimal solution when domain is symmetric

Document Type : Original Paper

Authors

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

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.

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References

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[3] Burton, G.R. (1987). Rearrangements of Functions, Maximization of Convex Functionals, and Vortex Rings, Math. Ann., 276, 225-253.
[4] Burton, G.R. (1989). Variational problems on classes of rearrangements and multiple configurations for steady vortices, Ann. Inst. Henri Poincare, 6, 295-319.
[5] Kawohl, B. (1985). Rearrangements and Convexity of Level Sets in PDE, Lectures Notes in Mathematics, 1150, Berlin.
[6] Zivari-Rezapour, M. (2013). Maximax rearrangement optimization related to a homogeneous Dirichlet problem, Arab. J. Math. 2, 427-433.
Journal of Advanced Mathematical Modeling
Volume 6, Issue 1
April 2016
Pages 81-88

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History

  • Receive Date: 19 January 2016
  • Revise Date: 17 August 2016
  • Accept Date: 08 September 2016

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