Existence and non-existence results for fully nonlinear elliptic systems

Alexander Quaas (1) , Boyan Sirakov (2, 3)

1 Departamento de Matematica [Valparaiso]
2 MODAL'X - Modélisation aléatoire de Paris X
3 CAMS - Centre d'Analyse et de Mathématique sociales

We study systems of two elliptic equations, with right-hand sides with general power-like superlinear growth, and left-hand sides which are of Isaac's or Hamilton-Jacobi-Bellman type (however many of our results are new even for linear left-hand sides). We show that under appropriate growth conditions such systems have positive solutions and that all such solutions are bounded in the uniform norm.

Domaines: Equations aux dérivées partielles [math.AP]

Alexander Quaas, Boyan Sirakov. Existence and non-existence results for fully nonlinear elliptic systems. Indiana University Mathematics Journal, 2009, 58 (2), pp.751-788. ⟨hal-00138107v3⟩