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

被引：76

作者：

Birindelli, I.

Demengel, F.

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[2] Univ Cergy Pontoise, Lab Anal Geometrie & Modelisat, F-95302 Cergy Pontoise, France

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2007年 / 6卷 / 02期

关键词：

fully nonlinear equation; viscosity solution; eigenvalue;

D O I：

10.3934/cpaa.2007.6.335

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, 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.

引用

页码：335 / 366

页数：32

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