On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators

被引：23
|
作者：
Quaas, A
Sirakov, B
机构：
[1] Univ Tecn Federico Santa Maria, Dept Matemat, Valparaiso 110, Chile
[2] Univ Paris 10, SEGMI, UFR, F-92001 Nanterre, France
[3] CAMS, EHESS, F-75270 Paris 06, France
来源：
COMPTES RENDUS MATHEMATIQUE | 2006年 / 342卷 / 02期
关键词：
D O I：
10.1016/j.crma.2005.11.003
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; - obtain existence and uniqueness results for non-proper operators whose principal eigenvalues (in some cases, only one of them) are positive; - obtain an existence result for non-proper Isaac's equations. To cite this article: A. Quaas, B. Sirakov, C R. Acad. Sci. Paris, Ser. 1342 (2006). (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.
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页码：115 / 118
页数：4
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