EIGENVALUE, MAXIMUM PRINCIPLE AND REGULARITY FOR FULLY NON LINEAR HOMOGENEOUS OPERATORS

Isabeau Birindelli (1) , Françoise Demengel (2)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

The main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic, homogenous with lower order terms. In particular we prove maximum and comparison principle, H ̈older and Lipschitz regularity. This leads to the existence of a first eigenvalue and eigenfunction and to the existence of solutions of Dirichlet problems within this class of operators.

Mots clés: Fully nonlinear operators; eigenvalue

Domaines: Equations aux dérivées partielles [math.AP]

Isabeau Birindelli, Françoise Demengel. EIGENVALUE, MAXIMUM PRINCIPLE AND REGULARITY FOR FULLY NON LINEAR HOMOGENEOUS OPERATORS. Communications on Pure and Applied Analysis, 2007, 6 (2), pp.335-366. ⟨hal-00842117⟩