-
Previous Article
Existence and uniqueness of entropy solutions to strongly degenerate parabolic equations with discontinuous coefficients
- PROC Home
- This Issue
-
Next Article
Existence of solutions to a multi-point boundary value problem for a second order differential system via the dual least action principle
On the uniqueness of blow-up solutions of fully nonlinear elliptic equations
| 1. | Department of Mathematics, University of Salerno, 84084 Fisciano (SA), Italy, Italy, Italy |
- Abstract
- Related Papers
Under a Creative Commons license
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), 573-612. |
| [2] |
L. A. Caffarelli and X. Cabré, "Fully Nonlinear Elliptic Equations'', Colloquium Publications 43, American Mathematical Society, Providence, 1995. |
| [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), 365-398. |
| [4] |
I. Capuzzo Dolcetta and A. Vitolo, Glaeser's type gradient estimates for non-negative solutions of fully nonlinear elliptic equations, Discrete Contin. Dyn. Syst., 28 (2010), 539-557. |
| [5] |
M. G. Crandall, H.Ishii and P. L. Lions, User's guide to viscosity solutions of second-order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), 1-67. |
| [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), 1-20. |
| [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), 121-127. |
| [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), 317-330. |
| [9] |
H. Dong, S. Kim and M. Safonov, On uniqueness boundary blow-up solutions of a class of nonlinear elliptic equations, Commun. Partial Differ. Equations, 33 (2008), 177-188. |
| [10] |
L. Escauriaza, $W^{2,n}$ a priori estimates for solutions to fully nonlinear equations, Indiana Univ. Math. J., 42 (1993), 413-423. |
| [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), 125-141. |
| [12] |
G. Galise and A. Vitolo, Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity, Int. J. Differ. Equ., 2011, Article ID 453727, 18 pp. |
| [13] |
H. Ishii and P. L. Lions, Viscosity Solutions of Fully Nonlinear Second-Order Elliptic Equations, J. Differential Equations, 83 (1990), 26-78. |
| [14] |
S. Koike, "A Beginners Guide to the Theory of Viscosity Solutions'', MSJ Memoirs 13, Math. Soc. Japan, Tokyo, 2004. |
| [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), 559-563. |
| [16] |
M. Marcus and L. Véron, Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. Henri Poincaré,Analyse non linéaire, 14 (1997), 237-274. |
| [17] |
M. H. Protter and H. F. Weinberger, "Maximum principles in Differential Equations'', Springer-Verlag, New York, 1984. |
| [18] |
P. Pucci and J. Serrin, "The maximum principles'', Progress in Nonlinear Differential Equations and Their Applications 73, Birkhäuser Verlag, Basel, 2007. |
| [19] |
B. Sirakov, Solvability of uniformly elliptic fully nonlinear PDE, Arch. Ration. Mech. Anal., 195 (2010), 579-607. |
| [20] |
A. Swiech, $W^{1,p}$-interior estimates for solutions of fully nonlinear, uniformly elliptic equations, Adv. Differential Equations, 2 (1997), 1005-1027. |
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), 573-612. |
| [2] |
L. A. Caffarelli and X. Cabré, "Fully Nonlinear Elliptic Equations'', Colloquium Publications 43, American Mathematical Society, Providence, 1995. |
| [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), 365-398. |
| [4] |
I. Capuzzo Dolcetta and A. Vitolo, Glaeser's type gradient estimates for non-negative solutions of fully nonlinear elliptic equations, Discrete Contin. Dyn. Syst., 28 (2010), 539-557. |
| [5] |
M. G. Crandall, H.Ishii and P. L. Lions, User's guide to viscosity solutions of second-order partial differential equations, Bull. Amer. Math. Soc., 27 (1992), 1-67. |
| [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), 1-20. |
| [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), 121-127. |
| [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), 317-330. |
| [9] |
H. Dong, S. Kim and M. Safonov, On uniqueness boundary blow-up solutions of a class of nonlinear elliptic equations, Commun. Partial Differ. Equations, 33 (2008), 177-188. |
| [10] |
L. Escauriaza, $W^{2,n}$ a priori estimates for solutions to fully nonlinear equations, Indiana Univ. Math. J., 42 (1993), 413-423. |
| [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), 125-141. |
| [12] |
G. Galise and A. Vitolo, Viscosity Solutions of Uniformly Elliptic Equations without Boundary and Growth Conditions at Infinity, Int. J. Differ. Equ., 2011, Article ID 453727, 18 pp. |
| [13] |
H. Ishii and P. L. Lions, Viscosity Solutions of Fully Nonlinear Second-Order Elliptic Equations, J. Differential Equations, 83 (1990), 26-78. |
| [14] |
S. Koike, "A Beginners Guide to the Theory of Viscosity Solutions'', MSJ Memoirs 13, Math. Soc. Japan, Tokyo, 2004. |
| [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), 559-563. |
| [16] |
M. Marcus and L. Véron, Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. Henri Poincaré,Analyse non linéaire, 14 (1997), 237-274. |
| [17] |
M. H. Protter and H. F. Weinberger, "Maximum principles in Differential Equations'', Springer-Verlag, New York, 1984. |
| [18] |
P. Pucci and J. Serrin, "The maximum principles'', Progress in Nonlinear Differential Equations and Their Applications 73, Birkhäuser Verlag, Basel, 2007. |
| [19] |
B. Sirakov, Solvability of uniformly elliptic fully nonlinear PDE, Arch. Ration. Mech. Anal., 195 (2010), 579-607. |
| [20] |
A. Swiech, $W^{1,p}$-interior estimates for solutions of fully nonlinear, uniformly elliptic equations, Adv. Differential Equations, 2 (1997), 1005-1027. |
| [1] |
Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 395-415. doi: 10.3934/cpaa.2004.3.395 |
| [2] |
Shigeaki Koike, Andrzej Świech. Local maximum principle for $L^p$-viscosity solutions of fully nonlinear elliptic PDEs with unbounded coefficients. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1897-1910. doi: 10.3934/cpaa.2012.11.1897 |
| [3] |
Françoise Demengel, O. Goubet. Existence of boundary blow up solutions for singular or degenerate fully nonlinear equations. Communications on Pure and Applied Analysis, 2013, 12 (2) : 621-645. doi: 10.3934/cpaa.2013.12.621 |
| [4] |
Huyuan Chen, Hichem Hajaiej, Ying Wang. Boundary blow-up solutions to fractional elliptic equations in a measure framework. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 1881-1903. doi: 10.3934/dcds.2016.36.1881 |
| [5] |
Zhifu Xie. General uniqueness results and examples for blow-up solutions of elliptic equations. Conference Publications, 2009, 2009 (Special) : 828-837. doi: 10.3934/proc.2009.2009.828 |
| [6] |
Zhijun Zhang, Ling Mi. Blow-up rates of large solutions for semilinear elliptic equations. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1733-1745. doi: 10.3934/cpaa.2011.10.1733 |
| [7] |
Marius Ghergu, Vicenţiu Rădulescu. Nonradial blow-up solutions of sublinear elliptic equations with gradient term. Communications on Pure and Applied Analysis, 2004, 3 (3) : 465-474. doi: 10.3934/cpaa.2004.3.465 |
| [8] |
Claudia Anedda, Giovanni Porru. Second order estimates for boundary blow-up solutions of elliptic equations. Conference Publications, 2007, 2007 (Special) : 54-63. doi: 10.3934/proc.2007.2007.54 |
| [9] |
Limei Dai. Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1707-1714. doi: 10.3934/cpaa.2011.10.1707 |
| [10] |
Lidan Wang, Lihe Wang, Chunqin Zhou. Classification of positive solutions for fully nonlinear elliptic equations in unbounded cylinders. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1241-1261. doi: 10.3934/cpaa.2021019 |
| [11] |
Laurent Di Menza, Olivier Goubet. Stabilizing blow up solutions to nonlinear schrÖdinger equations. Communications on Pure and Applied Analysis, 2017, 16 (3) : 1059-1082. doi: 10.3934/cpaa.2017051 |
| [12] |
Türker Özsarı. Blow-up of solutions of nonlinear Schrödinger equations with oscillating nonlinearities. Communications on Pure and Applied Analysis, 2019, 18 (1) : 539-558. doi: 10.3934/cpaa.2019027 |
| [13] |
Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 763-800. doi: 10.3934/dcds.2008.21.763 |
| [14] |
Chuanqiang Chen. On the microscopic spacetime convexity principle for fully nonlinear parabolic equations II: Spacetime quasiconcave solutions. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4761-4811. doi: 10.3934/dcds.2016007 |
| [15] |
Chuanqiang Chen. On the microscopic spacetime convexity principle of fully nonlinear parabolic equations I: Spacetime convex solutions. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3383-3402. doi: 10.3934/dcds.2014.34.3383 |
| [16] |
Jorge A. Esquivel-Avila. Blow-up in damped abstract nonlinear equations. Electronic Research Archive, 2020, 28 (1) : 347-367. doi: 10.3934/era.2020020 |
| [17] |
Victor A. Galaktionov, Juan-Luis Vázquez. The problem Of blow-up in nonlinear parabolic equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 399-433. doi: 10.3934/dcds.2002.8.399 |
| [18] |
Júlia Matos. Unfocused blow up solutions of semilinear parabolic equations. Discrete and Continuous Dynamical Systems, 1999, 5 (4) : 905-928. doi: 10.3934/dcds.1999.5.905 |
| [19] |
Italo Capuzzo Dolcetta, Antonio Vitolo. Glaeser's type gradient estimates for non-negative solutions of fully nonlinear elliptic equations. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 539-557. doi: 10.3934/dcds.2010.28.539 |
| [20] |
Luca Rossi. Non-existence of positive solutions of fully nonlinear elliptic equations in unbounded domains. Communications on Pure and Applied Analysis, 2008, 7 (1) : 125-141. doi: 10.3934/cpaa.2008.7.125 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]