Principal eigenvalues and the Dirichlet problem for fully nonlinear operators

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 prove the existence of two principal eigenvalues and eigenfunctions for 1-homogeneous convex uniformly elliptic fully nonlinear operators, study their properties, and discuss related Dirichlet problems.

Domaines: Equations aux dérivées partielles [math.AP]

Alexander Quaas, Boyan Sirakov. Principal eigenvalues and the Dirichlet problem for fully nonlinear operators. Advances in Mathematics, 2008, 218 (1), pp.105-135. ⟨hal-00004692v3⟩