# American Institute of Mathematical Sciences

June  2007, 6(2): 335-366. doi: 10.3934/cpaa.2007.6.335

## Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators

 1 Dipartimento di Matematica, Università di Roma 2 Laboratoire d'Analyse, Géométrie et Modelisation, Université de Cergy-Pontoise, Site de Saint-Martin, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise, France

Received  February 2006 Revised  November 2006 Published  March 2007

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, Hölder 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.
Citation: Isabeau Birindelli, Francoise Demengel. Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators. Communications on Pure and Applied Analysis, 2007, 6 (2) : 335-366. doi: 10.3934/cpaa.2007.6.335
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