M. Aizenman and P. Martin, Structure of gibbs states of one dimensional Coulomb systems, Communications in Mathematical Physics, vol.31, issue.1, pp.99-116, 1980.
DOI : 10.1007/BF01941972

G. Alberti, R. Choksi, and F. Otto, Uniform energy distribution for an isoperimetric problem with long-range interactions, Journal of the American Mathematical Society, vol.22, issue.2, pp.569-605, 2009.
DOI : 10.1090/S0894-0347-08-00622-X

Y. Ameur and J. Ortega-cerdà, Beurling???Landau densities of weighted Fekete sets and correlation kernel estimates, Journal of Functional Analysis, vol.263, issue.7, pp.1825-1861, 2012.
DOI : 10.1016/j.jfa.2012.06.011

A. Borodin and S. Serfaty, Renormalized Energy Concentration in Random Matrices, Communications in Mathematical Physics, vol.177, issue.3, pp.199-244, 2013.
DOI : 10.1007/s00220-013-1716-z

URL : https://hal.archives-ouvertes.fr/hal-00667652

H. J. Brascamp and E. H. Lieb, Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma, Functional integration and its applications, A.M. Arthurs, 1975.
DOI : 10.1007/978-3-642-55925-9_34

L. Caffarelli, The obstacle problem revisited, The Journal of Fourier Analysis and Applications, vol.46, issue.1, pp.383-402, 1998.
DOI : 10.1007/BF02498216

P. Grisvard, Elliptic problems in nonsmooth domains, 1985.
DOI : 10.1137/1.9781611972030

B. Jancovici, J. Lebowitz, and G. Manificat, Large charge fluctuations in classical Coulomb systems, Journal of Statistical Physics, vol.28, issue.3-4, pp.773-787, 1993.
DOI : 10.1007/BF01048032

H. Kunz, The one-dimensional classical electron gas, Annals of Physics, vol.85, issue.2, pp.303-335, 1974.
DOI : 10.1016/0003-4916(74)90413-8

N. Lev and J. Ortega-cerdà, Equidistribution estimates for Fekete points on complex manifolds, Journal of the European Mathematical Society, vol.18, issue.2
DOI : 10.4171/JEMS/594

N. Rougerie and S. Serfaty, Higher-Dimensional Coulomb Gases and Renormalized Energy Functionals, Communications on Pure and Applied Mathematics, vol.62, issue.3
DOI : 10.1002/cpa.21570

URL : https://hal.archives-ouvertes.fr/hal-00843042

E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Grundlehren der mathematischen Wissenchaften 316, 1997.

E. Sandier and S. Serfaty, From the Ginzburg-Landau Model to Vortex Lattice Problems, Communications in Mathematical Physics, vol.262, issue.1, pp.635-743, 2012.
DOI : 10.1007/s00220-012-1508-x

URL : https://hal.archives-ouvertes.fr/hal-00665987

E. Sandier and S. Serfaty, 1D log gases and the renormalized energy: crystallization at vanishing temperature, Probability Theory and Related Fields, vol.62, issue.3
DOI : 10.1007/s00440-014-0585-5

URL : https://hal.archives-ouvertes.fr/hal-01076972

S. Serfaty and I. Tice, LORENTZ SPACE ESTIMATES FOR THE COULOMBIAN RENORMALIZED ENERGY, Communications in Contemporary Mathematics, vol.14, issue.04, p.1250027, 2012.
DOI : 10.1142/S0219199712500277