Geodesic
Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent
Caju, Rayssa1 ; do Ó, João Marcos2 ; Santos, Almir Silva3
1 Department of Mathematics, Federal University of Paraíba, 58051-900, João Pessoa-PB, Brazil
2 Department of Mathematics, Brasília University, 70910-900, Brasília, DF, Brazil
3 Department of Mathematics, Federal University of Sergipe, 49100-000, São Cristovão-SE, Brazil
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 6, pp. 1575-1601

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We studied the asymptotic behavior of local solutions for strongly coupled critical elliptic systems near an isolated singularity. For the dimension less than or equal to five we prove that any singular solution is asymptotic to a rotationally symmetric Fowler type solution. This result generalizes the celebrated work due to Caffarelli, Gidas and Spruck [1] who studied asymptotic proprieties to the classic Yamabe equation. In addition, we generalize similar results by Marques [12] for inhomogeneous context, that is, when the metric is not necessarily conformally flat.

DOI : 10.1016/j.anihpc.2019.02.001
Classification : 35J60, 35B40, 35B33, 53C21
Keywords: Critical equations, Elliptic systems, Asymptotic symmetry, Singular solution, A priori estimate

Caju, Rayssa 1 ; do Ó, João Marcos 2 ; Santos, Almir Silva 3

1 Department of Mathematics, Federal University of Paraíba, 58051-900, João Pessoa-PB, Brazil
2 Department of Mathematics, Brasília University, 70910-900, Brasília, DF, Brazil
3 Department of Mathematics, Federal University of Sergipe, 49100-000, São Cristovão-SE, Brazil 
@article{AIHPC_2019__36_6_1575_0,
     author = {Caju, Rayssa and do \'O, Jo\~ao Marcos and Santos, Almir Silva},
     title = {Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1575--1601},
     publisher = {Elsevier},
     volume = {36},
     number = {6},
     year = {2019},
     doi = {10.1016/j.anihpc.2019.02.001},
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     zbl = {1425.35039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.02.001/}
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Caju, Rayssa; do Ó, João Marcos; Santos, Almir Silva. Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 6, pp. 1575-1601. doi: 10.1016/j.anihpc.2019.02.001

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