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Sharp decay estimates and smoothness for solutions to nonlocal semilinear equations
Boundary blow-up solutions to fractional elliptic equations in a measure framework
1. | Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China, China |
2. | Department of Mathematics, King Saud University, P.O. Box 2455, 11451 Riyadh |
References:
[1] |
C. Bandle and M. Marcus, Asymptotic behaviour of solutions and derivatives for semilinear elliptic problems with blow-up on the boundary, Ann. Inst. H. Poincaré Anal. Non Linéaire, 12 (1995), 155-171. |
[2] |
Ph. Bénilan, H. Brezis and M. Crandall, A semilinear elliptic equation in $L^1(\mathbbR^N )$, Ann. Sc. Norm. Sup. Pisa Cl. Sci., 2 (1975), 523-555. |
[3] |
L. Caffarelli and L. Silvestre, Regularity theory for fully nonlinear integro-differential equaitons, Comm. Pure Appl. Math., 62 (2009), 597-638.
doi: 10.1002/cpa.20274. |
[4] |
Z. Chen and R. Song, Estimates on Green functions and poisson kernels for symmetric stable process, Math. Ann., 312 (1998), 465-501.
doi: 10.1007/s002080050232. |
[5] |
H. Chen, P. Felmer and A. Quaas, Large solution to elliptic equations involving fractional Laplacian,, accepted by Ann. Inst. H. Poincaré, ().
doi: 10.1016/j.anihpc.2014.08.001. |
[6] |
H. Chen and H. Hajaiej, Existence, Non-existence, Uniqueness of solutions for semilinear elliptic equations involving measures concentrated on boundary, arXiv:1410.2672 (2014). |
[7] |
R. Cignoli and M. Cottlar, An Introduction to Functional Analysis, North-Holland, Amsterdam, 1974. |
[8] |
H. Chen and L. Véron, Semilinear fractional elliptic equations involving measures, J. Differential equations, 257 (2014), 1457-1486.
doi: 10.1016/j.jde.2014.05.012. |
[9] |
Y. Du and Z. Guo, Uniqueness and layer analysis for boundary blow-up solutions, J. Math. Pures Appl., 83 (2004), 739-763.
doi: 10.1016/j.matpur.2004.01.006. |
[10] |
M. del Pino and R. Letelier, The influence of domain geometry in boundary blow-up elliptic problems, Nonlinear Analysis: Theory, Methods & Applications, 48 (2002), 897-904.
doi: 10.1016/S0362-546X(00)00222-4. |
[11] |
Y. Du, Z. Guo and F. Zhou, Boundary blow-up solutions with interior layers and spikes in a bistable problem, Discrete Contin. Dyn. Syst., 19 (2007), 271-298.
doi: 10.3934/dcds.2007.19.271. |
[12] |
P. Felmer and A. Quaas, Fundamental solutions and Liouville type theorems for nonlinear integral operators, Advances in Mathematics, 226 (2011), 2712-2738.
doi: 10.1016/j.aim.2010.09.023. |
[13] |
J. B. Keller, On solutions of $\Delta u = f(u)$, Comm. Pure Appl. Math., 10 (1957), 503-510.
doi: 10.1002/cpa.3160100402. |
[14] |
J. Garcia-Melián, R. Letelier and J. de Lis, Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up, Proc. Amer. Math. Soc., 129 (2001), 3593-3602.
doi: 10.1090/S0002-9939-01-06229-3. |
[15] |
Z. Guo and F. Zhou, Exact multiplicity for boundary blow-up solutions, J. Differential Equations, 228 (2006), 486-506.
doi: 10.1016/j.jde.2006.02.012. |
[16] |
R. Osserman, On the inequality $\Delta u = f(u)$, Pac. J. Math., 7 (1957), 1641-1647. |
[17] |
T. Ouyang and J. Shi, Exact multiplicity of positive solutions for a class of semilinear problems, J. Differential Equations, 146 (1998), 121-156.
doi: 10.1006/jdeq.1998.3414. |
[18] |
M. Pertti, Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511623813. |
[19] |
M. Marcus and L. Véron, Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. H. Poincaré, Analyse Non Linéaire, 14 (1997), 237-274.
doi: 10.1016/S0294-1449(97)80146-1. |
[20] |
M. Marcus and L. Véron, Existence and uniqueness results for large solutions of general nonlinear elliptic equation, J. Evol. Equ., 3 (2003), 637-652.
doi: 10.1007/s00028-003-0122-y. |
show all references
References:
[1] |
C. Bandle and M. Marcus, Asymptotic behaviour of solutions and derivatives for semilinear elliptic problems with blow-up on the boundary, Ann. Inst. H. Poincaré Anal. Non Linéaire, 12 (1995), 155-171. |
[2] |
Ph. Bénilan, H. Brezis and M. Crandall, A semilinear elliptic equation in $L^1(\mathbbR^N )$, Ann. Sc. Norm. Sup. Pisa Cl. Sci., 2 (1975), 523-555. |
[3] |
L. Caffarelli and L. Silvestre, Regularity theory for fully nonlinear integro-differential equaitons, Comm. Pure Appl. Math., 62 (2009), 597-638.
doi: 10.1002/cpa.20274. |
[4] |
Z. Chen and R. Song, Estimates on Green functions and poisson kernels for symmetric stable process, Math. Ann., 312 (1998), 465-501.
doi: 10.1007/s002080050232. |
[5] |
H. Chen, P. Felmer and A. Quaas, Large solution to elliptic equations involving fractional Laplacian,, accepted by Ann. Inst. H. Poincaré, ().
doi: 10.1016/j.anihpc.2014.08.001. |
[6] |
H. Chen and H. Hajaiej, Existence, Non-existence, Uniqueness of solutions for semilinear elliptic equations involving measures concentrated on boundary, arXiv:1410.2672 (2014). |
[7] |
R. Cignoli and M. Cottlar, An Introduction to Functional Analysis, North-Holland, Amsterdam, 1974. |
[8] |
H. Chen and L. Véron, Semilinear fractional elliptic equations involving measures, J. Differential equations, 257 (2014), 1457-1486.
doi: 10.1016/j.jde.2014.05.012. |
[9] |
Y. Du and Z. Guo, Uniqueness and layer analysis for boundary blow-up solutions, J. Math. Pures Appl., 83 (2004), 739-763.
doi: 10.1016/j.matpur.2004.01.006. |
[10] |
M. del Pino and R. Letelier, The influence of domain geometry in boundary blow-up elliptic problems, Nonlinear Analysis: Theory, Methods & Applications, 48 (2002), 897-904.
doi: 10.1016/S0362-546X(00)00222-4. |
[11] |
Y. Du, Z. Guo and F. Zhou, Boundary blow-up solutions with interior layers and spikes in a bistable problem, Discrete Contin. Dyn. Syst., 19 (2007), 271-298.
doi: 10.3934/dcds.2007.19.271. |
[12] |
P. Felmer and A. Quaas, Fundamental solutions and Liouville type theorems for nonlinear integral operators, Advances in Mathematics, 226 (2011), 2712-2738.
doi: 10.1016/j.aim.2010.09.023. |
[13] |
J. B. Keller, On solutions of $\Delta u = f(u)$, Comm. Pure Appl. Math., 10 (1957), 503-510.
doi: 10.1002/cpa.3160100402. |
[14] |
J. Garcia-Melián, R. Letelier and J. de Lis, Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up, Proc. Amer. Math. Soc., 129 (2001), 3593-3602.
doi: 10.1090/S0002-9939-01-06229-3. |
[15] |
Z. Guo and F. Zhou, Exact multiplicity for boundary blow-up solutions, J. Differential Equations, 228 (2006), 486-506.
doi: 10.1016/j.jde.2006.02.012. |
[16] |
R. Osserman, On the inequality $\Delta u = f(u)$, Pac. J. Math., 7 (1957), 1641-1647. |
[17] |
T. Ouyang and J. Shi, Exact multiplicity of positive solutions for a class of semilinear problems, J. Differential Equations, 146 (1998), 121-156.
doi: 10.1006/jdeq.1998.3414. |
[18] |
M. Pertti, Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press, 1995.
doi: 10.1017/CBO9780511623813. |
[19] |
M. Marcus and L. Véron, Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations, Ann. Inst. H. Poincaré, Analyse Non Linéaire, 14 (1997), 237-274.
doi: 10.1016/S0294-1449(97)80146-1. |
[20] |
M. Marcus and L. Véron, Existence and uniqueness results for large solutions of general nonlinear elliptic equation, J. Evol. Equ., 3 (2003), 637-652.
doi: 10.1007/s00028-003-0122-y. |
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