A. Ambroso, X. Fleury, B. Lucquin-desreux, and P. A. Raviart, Some remarks on a stationary Vlasov-Poisson system with source term arising in ion beam neutralization, 2000.

S. Baalrud and C. Hegna, Kinetic theory of the presheath and the Bohm criterion, Plasma Sources Science and Technology, vol.20, issue.2, 2013.
DOI : 10.1088/0963-0252/20/2/025013

H. Beresticky and T. Lachant-robert, Some properties of monotone rearrangement with applications to elliptic equations in cylinders, Mathematische Nachrichten, vol.266, issue.1, pp.3-19, 2004.
DOI : 10.1002/mana.200310139

D. Bohm, The characteristics of electrical discharges in magnetic fields, 1949.

R. Chalise and R. Khanal, A kinetic trajectory simulation for magnetized plasma sheath, Institute of Physics Publishing, 2012.

F. Chen, Introduction to Plasma Physics, 1974.

L. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 2010.

M. Feldman, S. Y. Ha, and M. Slemrod, A Geometric Level-Set Formulation of a Plasma-Sheath Interface, Archive for Rational Mechanics and Analysis, vol.13, issue.1, pp.81-123, 2005.
DOI : 10.1007/s00205-005-0368-3

Y. Güçlü, The plasma sheath for 1D-1V Vlasov-Poisson solvers, Invited talk at the Numkin 2013 Conference

Y. Guo, C. Shu, and T. , ZIE The dynamics of a plane diode SIAM, J. MATH. ANAL, vol.35, issue.6

H. Kohno, J. R. Myra, and D. A. Ippolito, Radio-frequency sheath-plasma interactions with magnetic field tangency points along the sheath surface, Physics of Plasmas, vol.20, issue.8, p.82514, 2013.
DOI : 10.1063/1.4818991

J. G. Laframboise, Theory of spherical and cylindrical Langmuir probes in a collision less, Maxwellian plasma at rest, Institute for Aerospace Studies, Maire, ´ Etablissement et comparaison de modèles fluides pour un plasma faiblement ionisé quasi-neutre. Détermination des conditions aux limitesàlimitesà la paroi Thèse de Doctorat, 1966.

G. Manfredi and S. Devaux, Magnetized plasma-wall transition. Consequences for wall sputtering and erosion, Institute of Physics Publishing, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00606151

R. E. Marshak, The Variational Method for Asymptotic Neutron Densities, Physical review, 1947.

P. A. Raviart and C. Greengard, A Boundary-Value problem for the stationary Vlasov-Poisson equations : The Plane Diode, Communications on Pure and Applied Mathematics, 1990.

K. Riemann, The Bohm criterion and sheath formation Phys. Plasmas, 1991.

T. E. Sheridan, Solution of the plasma-sheath equation with a cool Maxwellian ion source, Physics of Plasmas, vol.8, issue.9, 2001.
DOI : 10.1063/1.1391448

G. Stampachia and D. Kinderlehrer, An introduction to variational inequalities and their applications, 1980.

P. Stangeby, The Plasma Boundary of Magnetic Fusion Devices, 2000.

F. Valsaque and G. Manfredi, Numerical study of plasma???wall transition in an oblique magnetic field, Journal of Nuclear Materials, vol.290, issue.293, 2001.
DOI : 10.1016/S0022-3115(00)00454-2