Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 60, pp. 1-9.

Title: Optimization problems involving Poisson's equation in R^3
       
Authors: Fariba Bahrami (Univ. of Tabriz, Iran)
         Hossain Fazli (Univ. of Tabriz, Iran)

Abstract:
 In this article, we prove the existence of minimizers for
 integrals associated with a second-order elliptic problem.
 For this three-dimensional optimization problem, the admissible
 set is a rearrangement class of a given function.

Submitted February 16, 2011. Published May 10, 2011.
Math Subject Classifications: 49J20, 49K20.
Key Words: Rearrangements class; variational problem;
           Poisson's equation; energy functional; minimization.