Keller-Osserman estimates for some quasilinear elliptic systems

Marie-Françoise Bidaut-Véron (1) , Marta Garcia-Huidobro (2) , Cecilia Yarur (3)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 Departamento de Matemáticas [Santiago de Chile]
3 Departamento de Matematicas y CC - Departamento de Matematicas y CC

In this article we study quasilinear multipower systems of two equations of two types, in a domain $\Omega$ of R^{N} : with absorption terms, or mixed terms. Despite of the lack of comparison principle, we prove a priori estimates of Keller-Osserman type. Concerning the mixed system , we show that one of the solutions always satisfies Harnack inequality. In the case $\Omega$=B(0,1)\{0}, we also study the behaviour near 0 of the solutions of more general weighted systems, giving a priori estimates and removability results. Finally we prove the sharpness of the results.

Mots clés: Quasilinear elliptic systems; a priori estimates; large solutions; asymptotic behaviour; Harnack inequality

Domaines: Equations aux dérivées partielles [math.AP]

Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Cecilia Yarur. Keller-Osserman estimates for some quasilinear elliptic systems. Communications in Pure and Applied Analysis, 2013, 12 (4), pp.1547-1568. ⟨10.3934/cpaa.2012.12⟩. ⟨hal-00565280v2⟩