G. Alberti, Variational models for phase transitions, an approach via ?convergence, Calculus of variations and partial differential equations, pp.95-114, 1996.

L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, 2000.

L. Ambrosio and V. M. Tortorelli, On the approximation of free discontinuity problems, Boll. Un. Mat. Ital. B, vol.6, issue.71, pp.105-123, 1992.

L. Ambrosio, A. Lemenant, and G. Royer-carfagni, A Variational Model for Plastic Slip and Its Regularization via ??-Convergence, Journal of Elasticity, vol.25, issue.8, pp.201-235, 2013.
DOI : 10.1007/s10659-012-9390-5

F. Benmansour, G. Carlier, G. Peyré, and F. Santambrogio, Derivatives with respect to metrics and applications: subgradient marching algorithm, Numerische Mathematik, vol.2, issue.2, pp.357-381, 2010.
DOI : 10.1007/s00211-010-0305-8

URL : https://hal.archives-ouvertes.fr/hal-00360971

E. G. Birgin, J. M. Martínez, and M. Raydan, Nonmonotone Spectral Projected Gradient Methods on Convex Sets, SIAM Journal on Optimization, vol.10, issue.4, pp.1196-1211, 2000.
DOI : 10.1137/S1052623497330963

B. Bourdin, D. Bucur, and . Oudet, Optimal Partitions for Eigenvalues, SIAM Journal on Scientific Computing, vol.31, issue.6, pp.4100-4114, 2009.
DOI : 10.1137/090747087

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

G. Buttazzo, E. Mainini, and E. Stepanov, Stationary configurations for the average distance functional and related problems, Control & Cybernetics, vol.38, issue.4A, pp.1107-1130, 2009.

]. G. Buttazzo, ´. E. Oudet, and E. Stepanov, Optimal Transportation Problems with Free Dirichlet Regions, Variational methods for discontinuous structures, pp.41-65
DOI : 10.1007/978-3-0348-8193-7_4

URL : https://hal.archives-ouvertes.fr/hal-00384991

G. Buttazzo and F. Santambrogio, Asymptotical compliance optimization for connected networks, Networks and Heterogeneous Media, vol.2, issue.4, pp.761-777, 2007.
DOI : 10.3934/nhm.2007.2.761

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

G. Buttazzo and E. Stepanov, Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem, Ann. Sc. Norm. Super. Pisa Cl

G. Carlier, C. Jimenez, and F. Santambrogio, Optimal Transportation with Traffic Congestion and Wardrop Equilibria, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1330-1350, 2008.
DOI : 10.1137/060672832

URL : https://hal.archives-ouvertes.fr/hal-00361010

A. Chambolle, A. Giacomini, and M. Ponsiglione, Crack Initiation in Brittle Materials, Archive for Rational Mechanics and Analysis, vol.151, issue.4, pp.309-349, 2008.
DOI : 10.1007/s00205-007-0080-6

URL : https://hal.archives-ouvertes.fr/hal-00381652

G. Choquet, Cours d'analyse, Tome II: Topologie. Espaces topologiques et espaces métriques. Fonctions numériques. Espaces vectoriels topologiques. Deuxì emé edition, revue et corrigée. Masson et Cie, ´ Editeurs, 1969.

G. David, Singular sets of minimizers for the Mumford-Shah functional, Progress in Mathematics, vol.233, 2005.

I. Ekeland and R. Temam, Convex Analysis and Variational Problems, Studies in Mathematics and Its Applications, 1976.
DOI : 10.1137/1.9781611971088

H. Federer, Geometric measure theory Die Grundlehren der mathematischen Wissenschaften, 1969.

R. Fletcher, Practical Methods of Optimization, 1987.
DOI : 10.1002/9781118723203

M. Galassi, GNU Scientific Library Reference Manual

E. N. Gilbert and H. O. Pollak, Steiner Minimal Trees, SIAM Journal on Applied Mathematics, vol.16, issue.1, pp.1-29, 1968.
DOI : 10.1137/0116001

R. Karp, Reducibility among combinatorial problems, In Complexity of Computer Computations, pp.85-103, 1972.
DOI : 10.1007/978-3-540-68279-0_8

A. Lemenant, About the regularity of average distance minimizers in R 2, J. Convex Anal, vol.18, issue.4, pp.949-981, 2011.

A. Lemenant, A presentation of the average distance minimizing problem, Journal of Mathematical Sciences, vol.17, issue.2, pp.117-146, 2011.
DOI : 10.1007/s10958-012-0717-3

A. Lemenant and F. Santambrogio, A Modica-Mortola approximation for the steiner problem. preprint, available at cvgmt.sns.it, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00903972

X. Yang, L. , and D. Slep?ev, Properties of minimizers of average-distance problem via discrete approximation of measures, SIAM J. Math. Anal, vol.45, issue.5, pp.3114-3131, 2013.

G. , D. Maso, and F. Iurlano, Fracture models as ??limits of damage models, Comm. Pure Appl. Anal, vol.12, issue.4, pp.1657-1686, 2013.

P. Mattila, Geometry of sets and measures in Euclidean spaces, volume 44 of Cambridge Studies in Advanced Mathematics, Fractals and rectifiability, 1995.

L. Modica, S. Mortola, and . Il-limite-nella-?-convergenza-di-una-famiglia-di-funzionali-ellittici, Approximation of partitions of least perimeter by ?-convergence: around Kelvin's conjecture, Boll. Un. Mat. Ital. A Exp. Math, vol.14, issue.203, pp.526-529260, 1977.

´. E. Oudet and F. Santambrogio, A Modica-Mortola Approximation for Branched Transport and Applications, Archive for Rational Mechanics and Analysis, vol.10, issue.1, pp.115-142, 2011.
DOI : 10.1007/s00205-011-0402-6

E. Paolini and E. Stepanov, Existence and regularity results for the Steiner problem, Calculus of Variations and Partial Differential Equations, vol.100, issue.3, pp.837-860, 2013.
DOI : 10.1007/s00526-012-0505-4

F. Santambrogio, A Dacorogna-Moser approach to flow decomposition and minimal flow problems. preprint, available at cvgmt.sns.it, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00871623

F. Santambrogio and P. Tilli, Blow-up of optimal sets in the irrigation problem, Journal of Geometric Analysis, vol.2, issue.4, pp.343-362, 2005.
DOI : 10.1007/BF02922199

F. Santambrogio, A Modica???Mortola approximation for branched transport, Comptes Rendus Mathematique, vol.348, issue.15-16, pp.15-16941, 2010.
DOI : 10.1016/j.crma.2010.07.016

URL : https://hal.archives-ouvertes.fr/hal-00417461

J. A. Sethian, Level Set Methods and Fast Marching Methods, Cambridge Monographs on Applied and Computational Mathematics, 1999.

D. Slep?ev, Counterexample to regularity in average-distance problem, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.31, issue.1
DOI : 10.1016/j.anihpc.2013.02.004

E. Stepanov, Partial Geometric Regularity of Some Optimal Connected Transportation Networks, Journal of Mathematical Sciences, vol.12, issue.4, pp.522-552, 2006.
DOI : 10.1007/s10958-005-0514-3

P. Tilli, Some explicit examples of minimizers for the irrigation problem, J. Convex Anal, vol.17, issue.2, pp.583-595, 2010.

J. N. Tsitsiklis, Efficient algorithms for globally optimal trajectories. Automatic Control, IEEE Transactions on, vol.40, issue.9, pp.1528-1538, 1995.