Solvability of monotone systems of fully nonlinear elliptic PDE's

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 quasimonotone systems of fully nonlinear uniformly elliptic equations. Our goal is, on one hand, to give a necessary and sufficient condition under which the system satisfies a comparison principle, and on the other hand, to give explicit conditions under which ordered sub- and supersolutions can be found, so Perron's method implies the existence of a solution. For a large class of systems our results are optimal. Further, we aim at proving results of existence of eigenvalues of vector fully nonlinear operators.

Domaines: Equations aux dérivées partielles [math.AP]

Alexander Quaas, Boyan Sirakov. Solvability of monotone systems of fully nonlinear elliptic PDE's. Comptes Rendus. Mathématique, 2008, 346 (11-12), pp.641-644. ⟨hal-00138111⟩