EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 18 / No 4 (October-December 2012) ESAIM: COCV, 18 4 (2012) 1049-1072 References
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. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.