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

Isabeau Birindelli; Francoise Demengel

doi:10.3934/cpaa.2007.6.335

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2007, Volume 6, Issue 2: 335-366. Doi: 10.3934/cpaa.2007.6.335

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

Isabeau Birindelli^1, and
Francoise Demengel²

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

Received: January 31, 2006

Revised: October 31, 2006

Published: May 2007

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Abstract

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.

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Mathematics Subject Classification: 35J60, 35P30.

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