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On the uniqueness of blowup solutions of fully nonlinear elliptic equations
1.  Department of Mathematics, University of Salerno, 84084 Fisciano (SA), Italy, Italy, Italy 
References:
[1] 
X. Cabré and L. A. Caffarelli, Interior $C^{2,\alpha}$ regularity theory for a class of nonconvex fully nonlinear elliptic equations,, J. Math. Pures Appl., 82 (2003), 573. Google Scholar 
[2] 
L. A. Caffarelli and X. Cabré, "Fully Nonlinear Elliptic Equations'',, Colloquium Publications 43, (1995). Google Scholar 
[3] 
L. A. Caffarelli, M. G. Crandall, M. Kocan and A. Swiech, On viscosity solutions of fully nonlinear equations with measurable ingredients,, Commun. Pure Appl. Math., 49 (1996), 365. Google Scholar 
[4] 
I. Capuzzo Dolcetta and A. Vitolo, Glaeser's type gradient estimates for nonnegative solutions of fully nonlinear elliptic equations,, Discrete Contin. Dyn. Syst., 28 (2010), 539. Google Scholar 
[5] 
M. G. Crandall, H.Ishii and P. L. Lions, User's guide to viscosity solutions of secondorder partial differential equations,, Bull. Amer. Math. Soc., 27 (1992), 1. Google Scholar 
[6] 
M. G. Crandall, M. Kocan, P. L. Lions and A. Swiech, Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations,, Electron. J. Differ. Equ., 24 (1999), 1. Google Scholar 
[7] 
M. G. Crandall and A. Swiech, A note on generalized maximum principles for elliptic and parabolic PDE,, Lecture Notes in Pure and Appl. Math., 235 (2003), 121. Google Scholar 
[8] 
F. Da Lio and B. Sirakov, Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations,, J. Eur. Math. Soc. (JEMS), 9 (2007), 317. Google Scholar 
[9] 
H. Dong, S. Kim and M. Safonov, On uniqueness boundary blowup solutions of a class of nonlinear elliptic equations,, Commun. Partial Differ. Equations, 33 (2008), 177. Google Scholar 
[10] 
L. Escauriaza, $W^{2,n}$ a priori estimates for solutions to fully nonlinear equations,, Indiana Univ. Math. J., 42 (1993), 413. Google Scholar 
[11] 
M. J. Esteban, P. L. Felmer and A. Quaas, Superlinear elliptic equations for fully nonlinear operators without growth restrictions for the data,, Proc. Edinb. Math. Soc., 53 (2010), 125. Google Scholar 
[12] 
G. Galise and A. Vitolo, Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity,, Int. J. Differ. Equ., 2011 (4537). Google Scholar 
[13] 
H. Ishii and P. L. Lions, Viscosity Solutions of Fully Nonlinear SecondOrder Elliptic Equations,, J. Differential Equations, 83 (1990), 26. Google Scholar 
[14] 
S. Koike, "A Beginners Guide to the Theory of Viscosity Solutions'',, MSJ Memoirs 13, (2004). Google Scholar 
[15] 
M. Marcus and L. Véron, Uniqueness of solutions with blowup at the boundary for a class of nonlinear elliptic equations,, C.R. Acad. Sci. Paris, 317 (1993), 559. Google Scholar 
[16] 
M. Marcus and L. Véron, Uniqueness and asymptotic behavior of solutions with boundary blowup for a class of nonlinear elliptic equations,, Ann. Inst. Henri Poincaré, 14 (1997), 237. Google Scholar 
[17] 
M. H. Protter and H. F. Weinberger, "Maximum principles in Differential Equations'',, SpringerVerlag, (1984). Google Scholar 
[18] 
P. Pucci and J. Serrin, "The maximum principles'',, Progress in Nonlinear Differential Equations and Their Applications 73, (2007). Google Scholar 
[19] 
B. Sirakov, Solvability of uniformly elliptic fully nonlinear PDE,, Arch. Ration. Mech. Anal., 195 (2010), 579. Google Scholar 
[20] 
A. Swiech, $W^{1,p}$interior estimates for solutions of fully nonlinear, uniformly elliptic equations,, Adv. Differential Equations, 2 (1997), 1005. Google Scholar 
show all references
References:
[1] 
X. Cabré and L. A. Caffarelli, Interior $C^{2,\alpha}$ regularity theory for a class of nonconvex fully nonlinear elliptic equations,, J. Math. Pures Appl., 82 (2003), 573. Google Scholar 
[2] 
L. A. Caffarelli and X. Cabré, "Fully Nonlinear Elliptic Equations'',, Colloquium Publications 43, (1995). Google Scholar 
[3] 
L. A. Caffarelli, M. G. Crandall, M. Kocan and A. Swiech, On viscosity solutions of fully nonlinear equations with measurable ingredients,, Commun. Pure Appl. Math., 49 (1996), 365. Google Scholar 
[4] 
I. Capuzzo Dolcetta and A. Vitolo, Glaeser's type gradient estimates for nonnegative solutions of fully nonlinear elliptic equations,, Discrete Contin. Dyn. Syst., 28 (2010), 539. Google Scholar 
[5] 
M. G. Crandall, H.Ishii and P. L. Lions, User's guide to viscosity solutions of secondorder partial differential equations,, Bull. Amer. Math. Soc., 27 (1992), 1. Google Scholar 
[6] 
M. G. Crandall, M. Kocan, P. L. Lions and A. Swiech, Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations,, Electron. J. Differ. Equ., 24 (1999), 1. Google Scholar 
[7] 
M. G. Crandall and A. Swiech, A note on generalized maximum principles for elliptic and parabolic PDE,, Lecture Notes in Pure and Appl. Math., 235 (2003), 121. Google Scholar 
[8] 
F. Da Lio and B. Sirakov, Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations,, J. Eur. Math. Soc. (JEMS), 9 (2007), 317. Google Scholar 
[9] 
H. Dong, S. Kim and M. Safonov, On uniqueness boundary blowup solutions of a class of nonlinear elliptic equations,, Commun. Partial Differ. Equations, 33 (2008), 177. Google Scholar 
[10] 
L. Escauriaza, $W^{2,n}$ a priori estimates for solutions to fully nonlinear equations,, Indiana Univ. Math. J., 42 (1993), 413. Google Scholar 
[11] 
M. J. Esteban, P. L. Felmer and A. Quaas, Superlinear elliptic equations for fully nonlinear operators without growth restrictions for the data,, Proc. Edinb. Math. Soc., 53 (2010), 125. Google Scholar 
[12] 
G. Galise and A. Vitolo, Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity,, Int. J. Differ. Equ., 2011 (4537). Google Scholar 
[13] 
H. Ishii and P. L. Lions, Viscosity Solutions of Fully Nonlinear SecondOrder Elliptic Equations,, J. Differential Equations, 83 (1990), 26. Google Scholar 
[14] 
S. Koike, "A Beginners Guide to the Theory of Viscosity Solutions'',, MSJ Memoirs 13, (2004). Google Scholar 
[15] 
M. Marcus and L. Véron, Uniqueness of solutions with blowup at the boundary for a class of nonlinear elliptic equations,, C.R. Acad. Sci. Paris, 317 (1993), 559. Google Scholar 
[16] 
M. Marcus and L. Véron, Uniqueness and asymptotic behavior of solutions with boundary blowup for a class of nonlinear elliptic equations,, Ann. Inst. Henri Poincaré, 14 (1997), 237. Google Scholar 
[17] 
M. H. Protter and H. F. Weinberger, "Maximum principles in Differential Equations'',, SpringerVerlag, (1984). Google Scholar 
[18] 
P. Pucci and J. Serrin, "The maximum principles'',, Progress in Nonlinear Differential Equations and Their Applications 73, (2007). Google Scholar 
[19] 
B. Sirakov, Solvability of uniformly elliptic fully nonlinear PDE,, Arch. Ration. Mech. Anal., 195 (2010), 579. Google Scholar 
[20] 
A. Swiech, $W^{1,p}$interior estimates for solutions of fully nonlinear, uniformly elliptic equations,, Adv. Differential Equations, 2 (1997), 1005. Google Scholar 
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