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Stationary configurations for the average distance functional and related problems. (English) Zbl 1239.49029

Summary: 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.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
80A20 Heat and mass transfer, heat flow (MSC2010)
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