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. ,
Harmonic function theory, Graduate Texts in Mathematics, vol.137, 2001. ,
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
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. ,
Functional analysis, Sobolev spaces and partial differential equations, 2011. ,
DOI : 10.1007/978-0-387-70914-7
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
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
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
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
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
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
Boundary blow up solutions for fractional elliptic equations, Asymptot. Anal, vol.78, issue.3, pp.123-144, 2012. ,
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
?-potentials, Classical and modern potential theory and applications, Adv. Sci. Inst. Ser. C Math. Phys. Sci, vol.430, pp.217-232, 1993. ,
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. ,
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
Problèmes aux limites non homogènes et applications, Travaux et Recherches Mathématiques, vol.1, issue.17, p.1968 ,
The sub-supersolution method for weak solutions, Proc. Amer, pp.2429-2438, 2008. ,
DOI : 10.1090/S0002-9939-08-09231-9
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
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
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
Sharp bounds on the density, Green function and jumping function of subordinate killed BM, Probab. Theory Relat, pp.606-628, 2004. ,
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
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
Elliptic equations involving measures, Stationary partial differential equations, Handb. Differ. Equ, vol.I, pp.593-712, 2004. ,
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