Stationary configurations for the average distance functional and   related problems
  For a functional defined on the class of closed one-dimensional connected subsets of ${\mathbb R}^n$ we consider the corresponding minimization problem and we give suitable first order necessary conditions of optimality. The cases studied here are the average distance functional arising in the mass transportation theory, and the energy related to an elliptic PDE. 
Giuseppe Buttazzo, Edoardo Mainini, Eugene Stepanov
math.OC math.AP