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

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

2006-09-21

arxiv.org/abs/math/0609612v1

Mathematics

Analysis of PDEs

37 pages, 0 figures

Scientific paper

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 and homogenous. In particular we prove maximum and comparison principle, Holder 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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