Stationary configurations for the average distance functional and related problems

• Autorzy: Buttazzo G. , Mainini E. , Stepanov E.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

average distance functional; Euler equation; stationary point

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 4A
• Strony: 1107--1130
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Buttazzo G.

autor

Mainini E.

autor

Stepanov E.

• Dipartimento di Matematica, Universita di Pisa Largo B. Pontecorvo 5, 56127 Pisa, Italy,

Bibliografia

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• BUTTAZZO, G. and STEPANOV, E. (2003) Optimal transportation networks as free Dirichlet regions in the Monge-Kantorovich problem. Ann. Scuola Norm. Sup. Pisa Cl. Sci. II (4), 631-678.
• BUTTAZZO, G. and STEPANOV, E. (2004) Minimization problems for average distance functionals. In: Calculus of variations: topics from the mathematical heritage of E. De Giorgi. Quad. Mat., 14, Dept. Math., Seconda Univ. Napoli, Caserta, 48-83.
• HENROT, A. and PIERRE, N. (2005) Variation et optimisation de formes: une analyse géométrique. Mathématiques et Applications, 48. Springer-Verlag, Berlin.
• MANTEGAZZA, C. and MENNUCCI, A. (2003) Hamilton-Jacobi equations and distance functions on Riemannian manifolds. Appl. Math. Optim. 47 (1), 1-25.
• PAOLINI, E. and STEPANOV, E. (2004) Qualitative properties of maximum distance minimizers and average distance minimizers in Rn. J. Math. Sciences (N.Y.) 122 (3), 105-122.
• SANTAMBROGIO, F. and TILLI, P. (2005) Blow-up of optimal sets in the irrigation problem. J. Geom. Anal. 15 (2), 343-362.
• STEPANOV, E. (2006) Partial geometric regularity of some optimal connected transportation networks. J. Math. Sciences (N.Y.) 132 (4), 522-552.