The ∞-eigenvalue problem

被引：191

作者：

Juutinen, P ^{[1
]}

Lindqvist, P

Manfredi, JJ

机构：

[1] Univ Jyvaskyla, Dept Math, Jyvaskyla 40351, Finland

[2] Norwegian Inst Technol, Dept Math, N-7034 Trondheim, Norway

[3] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 1999年 / 148卷 / 02期

关键词：

Eigenvalue Problem;

D O I：

10.1007/s002050050157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Euler-Lagrange equation of the nonlinear Rayleigh quotient (integral(Omega) /del u\\(p) dx) /(integral(Omega) /u\(p) dx) is -div (/del u\(p-2)del u) = Lambda(p)(p/)u\(p-2)u, where Lambda(p)(p) is the minimum value of the quotient. The limit as p --> infinity of these equations is found to be max {Lambda(infinity) - /del u(x)\/u(x), Delta(infinity)u(x) } = 0, where the constant Lambda(infinity) = lim(p-->infinity) Lambda p is the reciprocal of the maximum of the distance to the boundary of the domain Omega.

引用

页码：89 / 105

页数：17

共 9 条

[1] EXTENSION OF FUNCTIONS SATISFYING LIPSCHITZ CONDITIONS [J].