N. Abatangelo, Large s-harmonic functions and boundary blow-up solutions for the fractional Laplacian, Discr Very large solution for the fractional Laplacian: towards a fractional Keller-Osserman condition, Cont. Dyn. Syst. A, vol.35, issue.12, 2015.

S. Axler, P. Bourdon, and W. Ramey, Harmonic function theory, Graduate Texts in Mathematics, vol.137, 2001.

K. Bogdan, T. Byczkowski, T. Kulczycki, M. Ryznar, R. Song et al., Potential analysis of stable processes and its extensions, Lecture Notes in Mathematics, vol.1980, 2009.
DOI : 10.1007/978-3-642-02141-1

URL : https://hal.archives-ouvertes.fr/hal-00469763

M. Bonforte, Y. Sire, and J. L. Vázquez, Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains, Discrete Contin, Dyn. Syst, vol.35, issue.12, pp.5725-5767, 2015.

H. Brezis, Functional analysis, Sobolev spaces and partial differential equations, 2011.
DOI : 10.1007/978-0-387-70914-7

L. A. Caffarelli and P. R. Stinga, Fractional elliptic equations, Caccioppoli estimates and regularity, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.33, issue.3
DOI : 10.1016/j.anihpc.2015.01.004

A. Capella, J. Dávila, L. Dupaigne, and Y. Sire, Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations, Communications in Partial Differential Equations, vol.330, issue.8, pp.1353-1384, 2011.
DOI : 10.1080/03605308008820155

URL : https://hal.archives-ouvertes.fr/hal-01338485

H. Chen, P. Felmer, and A. Quaas, Large solutions to elliptic equations involving fractional Laplacian, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.32, issue.6, pp.1199-1228, 2015.
DOI : 10.1016/j.anihpc.2014.08.001

E. B. Davies, The equivalence of certain heat kernel and Green function bounds, Journal of Functional Analysis, vol.71, issue.1, pp.88-103, 1987.
DOI : 10.1016/0022-1236(87)90017-6

E. B. Davies and B. Simon, Ultracontractivity and the heat kernel for Schr??dinger operators and Dirichlet Laplacians, Journal of Functional Analysis, vol.59, issue.2, pp.335-395, 1984.
DOI : 10.1016/0022-1236(84)90076-4

A. Dhifli, H. Mâagli, and M. Zribi, On the subordinate killed B.M in bounded domains and existence results for nonlinear fractional Dirichlet problems, Mathematische Annalen, vol.18, issue.9, pp.259-291, 2012.
DOI : 10.1007/s00208-011-0642-7

P. Felmer and A. Quaas, Boundary blow up solutions for fractional elliptic equations, Asymptot. Anal, vol.78, issue.3, pp.123-144, 2012.

J. Glover, Z. R. Pop-stojanovic, M. Rao, H. ?iki?, R. Song et al., Harmonic functions of subordinate killed Brownian motion, Journal of Functional Analysis, vol.215, issue.2, pp.399-426, 2004.
DOI : 10.1016/j.jfa.2004.01.001

J. Glover, M. Rao, H. ?iki?, and R. Song, ?-potentials, Classical and modern potential theory and applications, Adv. Sci. Inst. Ser. C Math. Phys. Sci, vol.430, pp.217-232, 1993.

G. Grubb, Fractional Laplacians on domains, a development of Hörmander's theory of µ-transmission pseudodifferential operators, Regularity of spectral fractional Dirichlet and Neumann problems, pp.478-528, 2015.

Q. Guan, Integration by Parts Formula for Regional Fractional Laplacian, Communications in Mathematical Physics, vol.71, issue.11???12, pp.289-329, 2006.
DOI : 10.1007/s00220-006-0054-9

J. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Travaux et Recherches Mathématiques, vol.1, issue.17, p.1968

M. Montenegro and A. C. Ponce, The sub-supersolution method for weak solutions, Proc. Amer, pp.2429-2438, 2008.
DOI : 10.1090/S0002-9939-08-09231-9

C. Mou and Y. Yi, Interior Regularity for Regional Fractional Laplacian, Communications in Mathematical Physics, vol.60, issue.1, pp.233-251, 2015.
DOI : 10.1007/s00220-015-2445-2

R. Servadei and E. Valdinoci, On the spectrum of two different fractional operators, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.144, issue.04, pp.831-855, 2014.
DOI : 10.1017/S0308210512001783

L. Silvestre, Regularity of the obstacle problem for a fractional power of the laplace operator, Communications on Pure and Applied Mathematics, vol.30, issue.1, pp.67-112, 2007.
DOI : 10.1002/cpa.20153

R. Song, Sharp bounds on the density, Green function and jumping function of subordinate killed BM, Probab. Theory Relat, pp.606-628, 2004.

R. Song and Z. Vondra?ek, Potential theory of subordinate killed Brownian motion in a domain, Probability Theory and Related Fields, vol.125, issue.4, pp.578-592, 2003.
DOI : 10.1007/s00440-002-0251-1

J. L. Vázquez, Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators, Discrete and Continuous Dynamical Systems - Series S, vol.7, issue.4, pp.857-885, 2014.
DOI : 10.3934/dcdss.2014.7.857

L. Véron, Elliptic equations involving measures, Stationary partial differential equations, Handb. Differ. Equ, vol.I, pp.593-712, 2004.

Q. Zhang, The Boundary Behavior of Heat Kernels of Dirichlet Laplacians, Journal of Differential Equations, vol.182, issue.2, pp.416-430, 2002.
DOI : 10.1006/jdeq.2001.4112