[1]
|
L. Bougherara, J. Giacomoni and J. Hernández, Existence and regularity of weak solutions for singular semilinear elliptic problems, Preprint 2014.
|
[2]
|
M. G. Crandall, P. H. Rabinowitz, and L. Tartar, On a Dirichlet problem with a singular nonlinearity, Comm. Partial Differential Equations, 2 (1977), 193-222.
|
[3]
|
M. Del Pino, A global estimate for the gradient in a singular elliptic boundary value problem, Proc. Roy. Soc. Edinburgh Sect. A, 122 (1992), 341-352.
|
[4]
|
J. I. Díaz, J. Hernández and J. M. Rakotoson, On very weak positive solutions to some semilinear elliptic problems with simultaneous singular nonlinear and spatial dependence terms, Milan J. Math., 79 (2011), 233-245.
|
[5]
|
J. I. Díaz and J. M. Rakotoson, On the differentiability of very weak solutions with right-hand side data integrable with respect to the distance to the boundary, J. Funct. Anal., 257 (2009), 807-831.
|
[6]
|
J. I. Díaz and J. E. Saá, Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires. C. R. Acad. Sci. Paris Sér. I Math., 305 (1988), 321-324.
|
[7]
|
J. Giacomoni, H. Maagli and P. Sauvy, Existence of compact support solutions for a quasilinear and singular problem, Differential Integral Equations, 25(7-8) (2012), 629-656.
|
[8]
|
J. Giacomoni, I. Schindler and P. Takáč, Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 6 (2007), 117-158.
|
[9]
|
J. Giacomoni, I. Schindler and P. Takáč, $C^{0,\beta}$-regularity and singular quasilinear elliptic equations, C. R. Math. Acad. Sci. Paris, 350(7-8) (2012), 383-388.
|
[10]
|
S. M. Gomes, On a singular nonlinear elliptic problem, SIAM J. Math. Anal., 17 (1986), 1359-1369.
|
[11]
|
C. Gui and F. H. Lin, Regularity of an elliptic problem with a singular nonlinearity, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), 1021-1029.
|
[12]
|
J. Hernández, F. Mancebo and J. M. Vega, Positive solutions for singular nonlinear elliptic equations, Proc. Roy. Soc. Edinburgh Sect. A, 137 (2007), 41-62.
|
[13]
|
A. C. Lazer and P. J. McKenna, On a singular nonlinear elliptic boundary-value problem, Proc. Amer. Math. Soc., 111 (1991), 721-730.
|
[14]
|
G. Lieberman, Boundary regularity for solutions of degenerate elliptic equations. Nonlinear Analysis, 12 (1988), 1203-1219.
|
[15]
|
P. Lindqvist, On the equation div $(|\nabla u|^{p-2}\nabla u)+\lambda|u|^{p-2}u=0$, Proc. Amer. Math. Soc., 109 (1990), 157-164.
|
[16]
|
J. Serrin, Local behavior of solutions of quasi-linear equations. Acta Math., 111 (1964), 247-302.
|
[17]
|
P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, 51 (1984), 126-150.
|
[18]
|
J.L. Vázquez, A strong maximum principle for some quasilinear equations, Appl. Math. Opt., 12 (1984), 1992-2002.
|
[19]
|
Z. Zhang and J. Cheng, Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems, Nonlinear Anal., 57 (2004), 473-484.
|