Free Access
Issue
ESAIM: COCV
Volume 18, Number 4, October-December 2012
Page(s) 1049 - 1072
DOI https://doi.org/10.1051/cocv/2011190
Published online 16 January 2012
  1. L. Ambrosio and C. Mantegazza, Curvature and distance function from a manifold. J. Geom. Anal. 8 (1998) 723–748. Dedicated to the memory of Fred Almgren. [CrossRef] [MathSciNet] [Google Scholar]
  2. L. Ambrosio and V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence. Comm. Pure Appl. Math. 43 (1990) 999–1036. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Bucur, I. Fragalà and J. Lamboley, Optimal convex shapes for concave functionals. ESAIM : COCV (in press). [Google Scholar]
  4. G. Buttazzo and P. Guasoni, Shape optimization problems over classes of convex domains. J. Convex Anal. 4 (1997) 343–351. [Google Scholar]
  5. G. Buttazzo and F. Santambrogio, Asymptotical compliance optimization for connected networks. Netw. Heterog. Media 2 (2007) 761–777 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  6. G. Buttazzo and E. Stepanov, Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem. Ann. Scuola Norm. Super. Pisa Cl. Sci. 2 (2003) 631–678. [MathSciNet] [Google Scholar]
  7. G. Buttazzo, E. Oudet and E. Stepanov, Optimal transportation problems with free Dirichlet regions, in Variational methods for discontinuous structures, Progr. Nonlinear Differential Equations Appl. 51. Birkhäuser, Basel (2002) 41–65. [Google Scholar]
  8. G. Buttazzo, A. Pratelli, S. Solimini and E. Stepanov, Optimal urban networks via mass transportation, Lecture Notes in Mathematics 1961. Springer-Verlag, Berlin (2009). [Google Scholar]
  9. G. Buttazzo, E. Mainini and E. Stepanov, Stationary configurations for the average distance functional and related problems. Control Cybernet. 38 (2009) 1107–1130. [MathSciNet] [Google Scholar]
  10. M.C. Delfour and J.-P. Zolésio, Shape analysis via distance functions : local theory, in Boundaries, interfaces, and transitions (Banff, AB, 1995), CRM Proc. Lect. Notes 13. Amer. Math. Soc. Providence, RI (1998) 91–123. [Google Scholar]
  11. H. Federer, Curvature measures. Trans. Amer. Math. Soc. 93 (1959) 418–491. [CrossRef] [MathSciNet] [Google Scholar]
  12. H. Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153. Springer-Verlag New York Inc., New York (1969). [Google Scholar]
  13. A. Henrot and M. Pierre, Variation et optimisation de formes, Mathématiques & Applications (Berlin) [Mathematics & Applications] 48. Springer, Berlin (2005). Une analyse géométrique [a geometric analysis]. [Google Scholar]
  14. A. Lemenant, About the regularity of average distance minimizers in R2. J. Convex Anal. 18 (2011) 949–981. [Google Scholar]
  15. A. Lemenant, A presentation of the average distance minimizing problem. Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 390 (2010) 117–146 (Proceedings of St. Petersburg Seminar, available online at http://www.pdmi.ras.ru/znsl/2011/v390/abs117.html). [Google Scholar]
  16. C. Mantegazza and A. Mennucci, Hamilton-jacobi equations and distance functions on riemannian manifolds. Appl. Math. Optim. 47 (2003) 1–25. [CrossRef] [MathSciNet] [Google Scholar]
  17. L. Modica and S. Mortola, Il limite nella Γ-convergenza di una famiglia di funzionali ellittici. Boll. Un. Mat. Ital. A 14 (1977) 526–529. [MathSciNet] [Google Scholar]
  18. E. Paolini and E. Stepanov, Qualitative properties of maximum distance minimizers and average distance minimizers in Rn. J. Math. Sci. (N. Y.) 122 (2004) 3290–3309. Problems in mathematical analysis. [CrossRef] [MathSciNet] [Google Scholar]
  19. F. Santambrogio and P. Tilli, Blow-up of optimal sets in the irrigation problem. J. Geom. Anal. 15 (2005) 343–362. [CrossRef] [MathSciNet] [Google Scholar]
  20. L. Simon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis 3. Australian National University, Australian National University Centre for Mathematical Analysis, Canberra (1983). [Google Scholar]
  21. E. Stepanov, Partial geometric regularity of some optimal connected transportation networks. J. Math. Sci. (N.Y.) 132 (2006) 522–552. Problems in mathematical analysis. [CrossRef] [MathSciNet] [Google Scholar]
  22. P. Tilli, Some explicit examples of minimizers for the irrigation problem. J. Convex Anal. 17 (2010) 583–595. [Google Scholar]

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