On unique continuation principles for some elliptic systems
Moreira dos Santos, Ederson1 ; Nornberg, Gabrielle1 ; Soave, Nicola2
1 a Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil
2 b Dipartimento di Matematica, Politecnico di Milano, Italy
Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1667-1680.
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In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily positive) radial solutions for the Lane-Emden system posed in a ball, in the critical and supercritical regimes. Some of our results also apply to general fully nonlinear operators, such as Pucci's extremal operators, being new even for scalar equations.

Reçu le :
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.12.001
Classification : 35J47, 35J60, 35B06, 35B50
Mots-clés : Unique continuation, Elliptic system, Lane-Emden, Nonexistence
Moreira dos Santos, Ederson 1 ; Nornberg, Gabrielle 1 ; Soave, Nicola 2

1 a Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil
2 b Dipartimento di Matematica, Politecnico di Milano, Italy 
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Moreira dos Santos, Ederson; Nornberg, Gabrielle; Soave, Nicola. On unique continuation principles for some elliptic systems. Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1667-1680. doi : 10.1016/j.anihpc.2020.12.001. http://www.numdam.org/articles/10.1016/j.anihpc.2020.12.001/

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