Calculus of Variations and Geometric Measure Theory

G. Buttazzo - E. Mainini - E. Stepanov

Stationary configurations for the average distance functional and related problems

created by stepanov on 10 Feb 2009
modified by mainini on 18 Mar 2010


Published Paper

Inserted: 10 feb 2009
Last Updated: 18 mar 2010

Journal: Control Cybernet.
Volume: 38
Number: 4A
Pages: 1107-1130
Year: 2009


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

Keywords: average distance functional, Euler equation, stationary point