Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators

被引：92

作者：

Quaas, Alexander ^{[2
]}

Sirakov, Boyan ^{[1
,3
]}

机构：

[1] Univ Paris 10, UFR SEGMI, F-92001 Nanterre, France

[2] Univ Santa Maria, Dept Matemat, Valparaiso, Chile

[3] CNRS, EHESS, F-75270 Paris, France

来源：

ADVANCES IN MATHEMATICS | 2008年 / 218卷 / 01期

关键词：

fully nonlinear operators; principal eigenvalues; Dirichlet problem;

D O I：

10.1016/j.aim.2007.12.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study uniformly elliptic fully nonlinear equations of the type F(D(2)u, Du, u, x) = f (x). We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects; we obtain existence and uniqueness results for nonproper operators whose principal eigenvalues (in some cases, only one of them) are positive; finally, we obtain an existence result for nonproper Isaac's equations. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：105 / 135

页数：31

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