H. W. Alt and L. A. Caffarelli, Existence and regularity for a minimum problem with free boundary, J. Reine Angew. Math, vol.325, pp.105-144, 1981.

H. W. Alt, L. A. Caffarelli, and A. Friedman, Variational problems with two phases and their free boundaries, Transactions of the American Mathematical Society, vol.282, issue.2, pp.431-461, 1984.
DOI : 10.1090/S0002-9947-1984-0732100-6

H. Berestycki, L. A. Caffarelli, and L. Nirenberg, Uniform estimates for regularization of free boundary problems, Analysis and partial differential equations, pp.567-619, 1990.

L. A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. I. Lipschitz free boundaries are C 1,? , Rev. Mat, Iberoamericana, vol.3, pp.139-162, 1987.

L. A. Caffarelli, D. Jerison, and C. E. Kenig, Some New Monotonicity Theorems with Applications to Free Boundary Problems, The Annals of Mathematics, vol.155, issue.2, pp.155-369, 2002.
DOI : 10.2307/3062121

L. A. Caffarelli and J. L. Vázquez, A free-boundary problem for the heat equation arising in flame propagation, Transactions of the American Mathematical Society, vol.347, issue.2, pp.411-441, 1995.
DOI : 10.1090/S0002-9947-1995-1260199-7

L. Hauswirth, F. Hélein, and F. Pacard, On an overdetermined elliptic problem, Pacific Journal of Mathematics, vol.250, issue.2, pp.319-334, 2011.
DOI : 10.2140/pjm.2011.250.319
URL : https://hal.archives-ouvertes.fr/hal-00851578

C. Lederman and N. Wolanski, A two phase elliptic singular perturbation problem with a forcing term, Journal de Math??matiques Pures et Appliqu??es, vol.86, issue.6, pp.552-589, 2006.
DOI : 10.1016/j.matpur.2006.10.008

S. Mirrahimi, G. Barles, B. Perthame, and P. E. Souganidis, A Singular Hamilton--Jacobi Equation Modeling the Tail Problem, SIAM Journal on Mathematical Analysis, vol.44, issue.6
DOI : 10.1137/100819527

D. R. Moreira, Least Supersolution Approach to Regularizing Free Boundary Problems, Archive for Rational Mechanics and Analysis, vol.39, issue.3, pp.97-141, 2009.
DOI : 10.1007/s00205-008-0113-9
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.8850

B. Perthame and M. Gauduchon, Survival thresholds and mortality rates in adaptive dynamics: conciliating deterministic and stochastic simulations, Mathematical Medicine and Biology, vol.27, issue.3, pp.195-210, 2010.
DOI : 10.1093/imammb/dqp018
URL : https://hal.archives-ouvertes.fr/hal-00755201

J. Serrin, A symmetry problem in potential theory, Archive for Rational Mechanics and Analysis, vol.43, issue.4, pp.304-318, 1971.
DOI : 10.1007/BF00250468

E. V. Teixeira, A variational treatment for general elliptic equations of the flame propagation type: regularity of the free boundary, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.25, issue.4, pp.25-633, 2008.
DOI : 10.1016/j.anihpc.2007.02.006