The Neumann eigenvalue problem for the ∞-Laplacian

被引：15

作者：

Esposito, L. ^{[1
]}

Kawohl, B. ^{[2
]}

Nitsch, C. ^{[3
]}

Trombetti, C. ^{[3
]}

机构：

[1] Dipartimento Matemat & Informat, I-84084 Fisciano, SA, Italy

[2] Univ Cologne, Inst Math, D-50923 Cologne, Germany

[3] Dipartimento Matemat & Applicaz, I-80126 Naples, Italy

来源：

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2015年 / 26卷 / 02期

关键词：

Neumann eigenvalues; viscosity solutions; infinity Laplacian; POINCARE INEQUALITIES;

D O I：

10.4171/RLM/697

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The first nontrivial eigenfunction of the Neumann eigenvalue problem for the p-Laplacian, suitably normalized, converges to a viscosity solution of an eigenvalue problem for the infinity-Laplacian as p -> infinity. We show among other things that the limiting eigenvalue, at least for convex sets, is in fact the first nonzero eigenvalue of the limiting problem. We then derive a number of consequences, which are nonlinear analogues of well-known inequalities for the linear (2-)Laplacian.

引用

页码：119 / 134

页数：16

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