G. Barles, Regularity results for first-order Hamilton-Jacobi equations, Differential Integral Equations, vol.3, issue.2, pp.103-125, 1990.
DOI : 10.1016/s0294-1449(16)30415-2
URL : http://www.numdam.org/article/AIHPC_1984__1_5_325_0.pdf

G. Barles, A weak Bernstein method for fully nonlinear elliptic equations, Differential Integral Equations, vol.4, issue.2, pp.241-262, 1991.

G. Barles, Solutions de viscosité deséquationsdeséquations de Hamilton-Jacobi, 1994.

G. Barles, S. Biton, and O. Ley, A Geometrical Approach to the Study??of Unbounded Solutions??of Quasilinear Parabolic Equations, Archive for Rational Mechanics and Analysis, vol.162, issue.4, pp.287-325, 2002.
DOI : 10.1007/s002050200188

G. Barles, E. Chasseigne, and C. Imbert, Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations, 2007.

G. Barles, L. C. Evans, and P. E. Souganidis, Wavefront propagation for reaction diffusion systems of PDE. Duke Math, J, vol.61, pp.835-858, 1990.

G. Barles and B. Perthame, Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics, Recent Developements in Nonlinear Partial Differential Equations, pp.57-68, 2007.
DOI : 10.1090/conm/439/08463
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.496.7701

G. Barles and B. Perthame, Dirac concentrations in Lotka-Volterra parabolic PDEs, Indiana Univ. Math. J, vol.57, issue.7, pp.3275-3301, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00168404

G. Barles and P. E. Souganidis, A remark on the asymptotic behavior of the solution of the KPP equation, C. R. Acad. Sci. Paris Sér. I Math, vol.319, issue.7, pp.679-684, 1994.

G. Barles and P. E. Souganidis, Front propagation for reaction-diffusion equations arising in combustion theory, Asymptotic Analysis, vol.14, pp.277-292, 1997.
DOI : 10.1016/s0294-1449(16)30228-1
URL : http://www.numdam.org/article/AIHPC_1992__9_5_479_0.pdf

S. Benachour, M. Ben-artzi, and P. Laurençot, Sharp decay estimates and vanishing viscosity for diffusive Hamilton-Jacobi equations, Advances in Differential Equations 14, pp.1-25, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00337773

C. Brändle and E. Chasseigne, Large deviations estimates for some non-local equations I. fast decaying kernels and explicit bounds, 2008.

N. Champagnat, R. Ferrì, and S. Méléard, Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models, Theoretical Population Biology, vol.69, issue.3, pp.297-321, 2006.
DOI : 10.1016/j.tpb.2005.10.004
URL : https://hal.archives-ouvertes.fr/inria-00164784

N. Champagnat, R. Ferrì, and S. Méléard, Individual-Based Probabilistic Models of Adaptive Evolution and Various Scaling Approximations, Progress in Probability, pp.75-114, 2008.
DOI : 10.1007/978-3-7643-8458-6_6
URL : https://hal.archives-ouvertes.fr/hal-00011146

E. Chasseigne, The Dirichlet problem for some nonlocal diffusion equations, Differential Integral Equations, vol.20, pp.1389-1404, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00132526

M. G. Crandall, H. Ishii, and P. Lions, user's guide to viscosity solutions\\ of second order\\ partial differential equations, Bulletin of the American Mathematical Society, vol.27, issue.1, pp.1-67, 1992.
DOI : 10.1090/S0273-0979-1992-00266-5

L. Desvillettes, P. E. Jabin, S. Mischler, and G. , On selection dynamics for continuous structured populations, Communications in Mathematical Sciences, vol.6, issue.3, pp.729-747, 2008.
DOI : 10.4310/CMS.2008.v6.n3.a10
URL : https://hal.archives-ouvertes.fr/hal-00363138

O. Diekmann, A beginner's guide to adaptive dynamics, Mathematical Modelling of Population Dynamics, pp.47-86, 2004.
DOI : 10.4064/bc63-0-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.505.9298

O. Diekmann, P. E. Jabin, S. Mischler, and B. Perthame, The dynamics of adaptation: An illuminating example and a Hamilton???Jacobi approach, Theoretical Population Biology, vol.67, issue.4, pp.257-271, 2005.
DOI : 10.1016/j.tpb.2004.12.003

L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol.19, 1998.

W. H. Fleming and H. M. Soner, Controlled markov processes and vicosity solutions, Applications of Mathematiques, vol.25, 1993.

W. H. Fleming and P. E. Souganidis, PDE-viscosity solution approach to some problems of large deviations, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.4, pp.171-192, 1986.

S. A. Geritz, E. Kisdi, G. Mészena, and J. A. Metz, Dynamics of Adaptation and Evolutionary Branching, Physical Review Letters, vol.71, issue.10, pp.2024-2027, 1997.
DOI : 10.1103/PhysRevLett.71.4083
URL : http://pure.iiasa.ac.at/4950/1/WP-96-077.pdf

S. A. Geritz, E. Kisdi, G. Mészena, and J. A. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evolutionary Ecology, vol.34, issue.1, pp.35-57, 1998.
DOI : 10.1007/BF02409749

P. L. Lions, Regularizing effects for first-order hamilton-jacobi equations, Applicable Analysis, vol.32, issue.3-4, pp.283-307, 1985.
DOI : 10.1090/S0002-9947-1983-0690039-8

G. Meszéna, M. Gyllenberg, F. J. Jacobs, and J. A. Metz, Link between Population Dynamics and Dynamics of Darwinian Evolution, Physical Review Letters, vol.2, issue.7, p.78105, 2005.
DOI : 10.1103/PhysRevE.68.041903

J. A. Metz, S. A. Geritz, G. Meszéna, F. J. Jacobs, and J. S. Van-heerwaarden, Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. Stochastic and spatial structures of dynamical systems, pp.183-231, 1995.

B. Perthame, Transport equations in biology. Series 'Frontiers in Mathematics, 2007.

P. E. Souganidis, Front propagation: theory and applications, CIME course on 'viscosity solutions, Lecture Notes in Math, 1998.
DOI : 10.1007/bfb0094298