Juutinen, Petri; Lindqvist, Peter; Manfredi, Juan J. The \(\infty\)-eigenvalue problem. (English) Zbl 0947.35104 Arch. Ration. Mech. Anal. 148, No. 2, 89-105 (1999). The authors prove the remarkable result that as \(p\to\infty\) the Euler-Lagrange equation of the nonlinear Rayleigh quotient becomes \[ \max\Biggl\{\Lambda_\infty- {|\nabla u(x)|\over u(x)}, \Delta_\infty u(x)\Biggr\}= 0, \] where \(\Lambda_\infty= {1\over\max\{\text{dist}(x, \partial\Omega;x\in\Omega)\}}\) and \(\Delta_\infty u(x)= \sum^n_{i,j= 1} {\partial u\over\partial x_i} {\partial u\over\partial x_j} {\partial^2u\over\partial x_i\partial x_j}\) is the \(\infty\)-Laplacian. Reviewer: B.D.Sleeman (Leeds) Cited in 5 ReviewsCited in 106 Documents MSC: 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35B40 Asymptotic behavior of solutions to PDEs Keywords:Euler-Lagrange equation; nonlinear Rayleigh quotient PDF BibTeX XML Cite \textit{P. Juutinen} et al., Arch. Ration. Mech. Anal. 148, No. 2, 89--105 (1999; Zbl 0947.35104) Full Text: DOI OpenURL