D. R. Adams and L. I. Hedberg, Function spaces and potential theory, Grundlehren Math. Wissen, vol.314, 1996.
DOI : 10.1007/978-3-662-03282-4

C. Bandle and M. Marcus, Sur les solutions maximales deprobì emes elliptiques nonlinéaires: bornes isopérimétriques et comportement asymptotique, C. R. Acad. Sci. Paris Sér. I Math, vol.311, pp.91-93, 1990.

C. Bandle and M. Marcus, ???Large??? solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour, Journal d'Analyse Math??matique, vol.322, issue.1, pp.9-24, 1992.
DOI : 10.1007/BF02790355

C. Bandle and M. Marcus, Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.12, issue.2, pp.155-171, 1995.
DOI : 10.1016/S0294-1449(16)30162-7

C. Bandle and M. Marcus, On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problemsDifferential Integral Equations, pp.23-34, 1998.

P. Baras, Singularit??s ??liminables pour des ??quations semi-lin??aires, Annales de l???institut Fourier, vol.34, issue.1, pp.185-206, 1984.
DOI : 10.5802/aif.956

B. Ph and H. Brezis, Nonlinear problems related to the Thomas-Fermi equation, J. Evolution Eq, vol.3, pp.673-770, 2003.

H. Brezis, Semilinear equations in ? N without condition at infinity, Applied Mathematics & Optimization, vol.7, issue.1, pp.271-282, 1985.
DOI : 10.1007/BF01449045

H. Brezis and W. Strauss, Semilinear elliptic equations in L 1, J. Math. Soc. Japan, vol.25, pp.265-590, 1973.

J. Dhersin, L. Gall, and J. , Wiener's test for super-Brownian motion and the Brownian snake, Probability Theory and Related Fields, vol.108, issue.1, pp.103-129, 1997.
DOI : 10.1007/s004400050103

E. B. Dynkin and . Diffusions, Superdiffusions and Partial Differential Equations, 2002.
DOI : 10.1090/coll/050

E. B. Dynkin, Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations, 2004.
DOI : 10.1090/ulect/034

E. B. Dynkin and S. E. Kuznetsov, Superdiffusions and removable singularities for quasilinear partial differential equations, Communications on Pure and Applied Mathematics, vol.49, issue.2, pp.125-176, 1996.
DOI : 10.1002/(SICI)1097-0312(199602)49:2<125::AID-CPA2>3.0.CO;2-G

E. B. Dynkin and S. E. Kuznetsov, Solutions ofLu=u ?? dominated byL-harmonic functions, Journal d'Analyse Math??matique, vol.5, issue.4, pp.15-37, 1996.
DOI : 10.1007/BF02790202

E. B. Dynkin and S. E. Kuznetsov, Fine topology and fine trace on the boundary associated with a class of semilinear differential equations, Communications on Pure and Applied Mathematics, vol.51, issue.8, pp.897-936, 1998.
DOI : 10.1002/(SICI)1097-0312(199808)51:8<897::AID-CPA2>3.0.CO;2-0

B. Fuglede, Finely harmonic functions, Lecture Notes in Math, 1972.

S. E. Kuznetsov, ??-Moderate solutions of Lu = u?? and fine trace on the boundary, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.10, pp.1189-1194, 1998.
DOI : 10.1016/S0764-4442(98)80225-5

D. A. Labutin, Wiener regularity for large solutions of nonlinear equations, Arkiv f??r Matematik, vol.41, issue.2, pp.307-339, 2003.
DOI : 10.1007/BF02390818

J. F. Legall, The Brownian snake and solutions of ??u=u 2 in a domain, Probability Theory and Related Fields, vol.74, issue.3, pp.393-432, 1995.
DOI : 10.1007/BF01192468

J. F. Legall, Spatial branching processes, random snakes and partial differential equations, Boston, 1999.

A. C. Lazer and P. J. Mackenna, On a problem of Bieberbach and Rademacher, Nonlinear Anal, pp.327-335, 1993.

C. Loewner and L. Nirenberg, Partial differential equations invariant under conformal or projective transformations, Contributions to Analysis, L. Ahlfors et al eds, pp.245-272, 1972.

M. Marcus and L. Véron, Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.14, issue.2, pp.237-274, 1997.
DOI : 10.1016/S0294-1449(97)80146-1

M. Marcus and L. Véron, The Boundary Trace of Positive Solutions of Semilinear Elliptic Equations: the Subcritical Case, Archive for Rational Mechanics and Analysis, vol.144, issue.3, pp.201-231, 1998.
DOI : 10.1007/s002050050116
URL : https://hal.archives-ouvertes.fr/hal-00511277

M. Marcus and L. Véron, The boundary trace of positive solutions of semilinear elliptic equations: The supercritical case, Journal de Math??matiques Pures et Appliqu??es, vol.77, issue.5, pp.481-524, 1998.
DOI : 10.1016/S0021-7824(98)80028-7

M. Marcus and L. Véron, Removable singularities and boundary traces, Journal de Math??matiques Pures et Appliqu??es, vol.80, issue.9, pp.879-900, 2001.
DOI : 10.1016/S0021-7824(01)01209-0
URL : http://doi.org/10.1016/s0021-7824(01)01209-0

M. Marcus and L. Véron, Existence and uniqueness results for large solutions of general nonlinear elliptic equations, Journal of Evolution Equations, vol.3, issue.4, pp.637-652, 2003.
DOI : 10.1007/s00028-003-0122-y

M. Marcus and L. Véron, The boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption, Communications on Pure and Applied Mathematics, vol.353, issue.9, pp.689-731, 2003.
DOI : 10.1002/cpa.3037

M. Marcus and L. Véron, Capacitary estimates of positive solutions of semilinear elliptic equations with absorption, J. European Math. Soc, vol.6, pp.483-527, 2004.

B. Mselati, Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation, Memoirs of the American Mathematical Society, vol.168, issue.798, 2004.
DOI : 10.1090/memo/0798

L. Véron, Semilinear elliptic equations with uniform blow-up on the boundary, Journal d'Analyse Math??matique, vol.127, issue.1, pp.231-250, 1992.
DOI : 10.1007/BF02790229

L. Véron, Generalized boundary values problems for nonlinear elliptic equations, Elec. J. Diff. Equ. Conf, vol.06, pp.313-342, 2001.

M. Laboratoire-de, Faculté des Sciences Parc de Grandmont, 37200 Tours, FRANCE E-mail address: veronl@lmpt.univ-tours