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On the blowup boundary solutions of the Monge Ampére equation with singular weights
1.  Department of Mathematics, Zhejiang University, Hangzhou 310027, China 
References:
[1] 
Bandle and M. Marcus, Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior,, J. Anal. Math., 58 (1992), 9. 
[2] 
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear secondorder elliptic equations I. MongeAmpére equation,, Comm. Pure Appl. Math., 37 (1984), 369. 
[3] 
S. Y. Cheng and S. T. Yau, On the regularity of the MongeAmpére equation $det(\partial^2/\partial x_i\partial x_j) =F(x, u)$,, Comm. Pure Appl. Math., 30 (1977), 41. 
[4] 
S. Y. Cheng and S. T. Yau, On the existence of a complete Kahler metric on noncompact complex manifolds and regularity of Fefferman's equation,, Comm. Pure Appl. Math., 33 (1980), 507. 
[5] 
M. Chuaqui and C. Cortazar et al., Uniqueness and boundary behavior of large solutions to elliptic problems with weight,, Comm. on Pure and Applied Analysis, 3 (2004), 653. 
[6] 
F. C. Cirstea and Y. Du, General uniqueness results and variation speed for blowup solutions of elliptic equations,, Proc. Lond. Math. Soc., 91 (2005), 459. 
[7] 
F. C. Cirstea and V. Radulescu, Blowup boundary solutions of semilinear elliptic problems,, Nonlinear Analysis, 48 (2002), 521. 
[8] 
F. C. Cirstea and C. Trombetti, On the MongeAmpére equation with boundary blowup: existence, uniqueness and asymptotics,, Calc. Var. Partial Differential Equations, 31 (2008), 167. 
[9] 
J. GarcíaMelián and R. LetelierAlbornoz et al., Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blowup,, Proc. Amer. Math. Soc., 129 (2001), 3593. 
[10] 
M. Ghergu and V. Radulescu, Nonradial blowup solutions of sublinear elliptic equations with gradient term,, Comm. on Pure and Applied Analysis, 3 (2004), 465. 
[11] 
B. Guan and H. Y. Jian, On the MongeAmpére equation with infinite boundary value,, Pac. J. Math., 216 (2004), 77. 
[12] 
Y. Huang, Boundary asymptotical behavior of large solutions to Hessian equations,, Pacific J. Math., 244 (2010), 85. 
[13] 
H. Y. Jian, Hessian equations with infinite Dirichlet boundary,, Indiana Univ. Math. J., 55 (2006), 1045. 
[14] 
J. B. Keller, On solutions of $\Delta u =f(u)$,, Comm. Pure Appl. Math., 10 (1995), 503. 
[15] 
N. D. Kutev, Nontrivial solutions for the equations of MongeAmpére type,, J. Math. Anal. Appl., 132 (1988), 424. 
[16] 
A. C. Lazer and P. J. Mckenna, On Singular Boundary Value Problems for the MongeAmpére Operator,, J. Math. Anal. Appl., 197 (1996), 341. 
[17] 
J. LópezGómez, Optimal uniqueness theorems and exact blowup rates of large solutions,, J. Diff. Eqns, 224 (2006), 385. 
[18] 
J. Matero, The BieberbachRademacher problem for the MongeAmpére Operator,, Manuscripta Math., 91 (1996), 379. 
[19] 
A. Mohammed, On the existence of solutions to the MongeAmpére equation with infinite boundary values,, Proc. Amer. Math. Soc., 135 (2007), 141. 
[20] 
A. Mohammed, Existence and estimates of solutions to a singular Dirichlet problem for the MongeAmpére equation,, J. Math. Anal. Appl., 340 (2008), 1226. 
[21] 
H. T. Yang, Existence and nonexistence of blowup boundary solutions for sublinear elliptic equations,, J. Math. Anal. Appl., 314 (2006), 85. 
[22] 
Z. Zhang, Boundary blowup elliptic problems with nonlinear gradient terms and singular weights,, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 1403. 
show all references
References:
[1] 
Bandle and M. Marcus, Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behavior,, J. Anal. Math., 58 (1992), 9. 
[2] 
L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear secondorder elliptic equations I. MongeAmpére equation,, Comm. Pure Appl. Math., 37 (1984), 369. 
[3] 
S. Y. Cheng and S. T. Yau, On the regularity of the MongeAmpére equation $det(\partial^2/\partial x_i\partial x_j) =F(x, u)$,, Comm. Pure Appl. Math., 30 (1977), 41. 
[4] 
S. Y. Cheng and S. T. Yau, On the existence of a complete Kahler metric on noncompact complex manifolds and regularity of Fefferman's equation,, Comm. Pure Appl. Math., 33 (1980), 507. 
[5] 
M. Chuaqui and C. Cortazar et al., Uniqueness and boundary behavior of large solutions to elliptic problems with weight,, Comm. on Pure and Applied Analysis, 3 (2004), 653. 
[6] 
F. C. Cirstea and Y. Du, General uniqueness results and variation speed for blowup solutions of elliptic equations,, Proc. Lond. Math. Soc., 91 (2005), 459. 
[7] 
F. C. Cirstea and V. Radulescu, Blowup boundary solutions of semilinear elliptic problems,, Nonlinear Analysis, 48 (2002), 521. 
[8] 
F. C. Cirstea and C. Trombetti, On the MongeAmpére equation with boundary blowup: existence, uniqueness and asymptotics,, Calc. Var. Partial Differential Equations, 31 (2008), 167. 
[9] 
J. GarcíaMelián and R. LetelierAlbornoz et al., Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blowup,, Proc. Amer. Math. Soc., 129 (2001), 3593. 
[10] 
M. Ghergu and V. Radulescu, Nonradial blowup solutions of sublinear elliptic equations with gradient term,, Comm. on Pure and Applied Analysis, 3 (2004), 465. 
[11] 
B. Guan and H. Y. Jian, On the MongeAmpére equation with infinite boundary value,, Pac. J. Math., 216 (2004), 77. 
[12] 
Y. Huang, Boundary asymptotical behavior of large solutions to Hessian equations,, Pacific J. Math., 244 (2010), 85. 
[13] 
H. Y. Jian, Hessian equations with infinite Dirichlet boundary,, Indiana Univ. Math. J., 55 (2006), 1045. 
[14] 
J. B. Keller, On solutions of $\Delta u =f(u)$,, Comm. Pure Appl. Math., 10 (1995), 503. 
[15] 
N. D. Kutev, Nontrivial solutions for the equations of MongeAmpére type,, J. Math. Anal. Appl., 132 (1988), 424. 
[16] 
A. C. Lazer and P. J. Mckenna, On Singular Boundary Value Problems for the MongeAmpére Operator,, J. Math. Anal. Appl., 197 (1996), 341. 
[17] 
J. LópezGómez, Optimal uniqueness theorems and exact blowup rates of large solutions,, J. Diff. Eqns, 224 (2006), 385. 
[18] 
J. Matero, The BieberbachRademacher problem for the MongeAmpére Operator,, Manuscripta Math., 91 (1996), 379. 
[19] 
A. Mohammed, On the existence of solutions to the MongeAmpére equation with infinite boundary values,, Proc. Amer. Math. Soc., 135 (2007), 141. 
[20] 
A. Mohammed, Existence and estimates of solutions to a singular Dirichlet problem for the MongeAmpére equation,, J. Math. Anal. Appl., 340 (2008), 1226. 
[21] 
H. T. Yang, Existence and nonexistence of blowup boundary solutions for sublinear elliptic equations,, J. Math. Anal. Appl., 314 (2006), 85. 
[22] 
Z. Zhang, Boundary blowup elliptic problems with nonlinear gradient terms and singular weights,, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 1403. 
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