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Stationary configurations for the average distance functional and related problems

Buttazzo G., Mainini E., Stepanov E.

Control and Cybernetics

2009

Vol. 38, no 4A

1107-1130

For a functional defined on the class of closed one-dimensional connected subsets of Rn 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.