## Differential and Integral Equations

### Limit as $p\to\infty$ of $p$-Laplace eigenvalue problems and $L^\infty$-inequality of the Poincaré type

#### Abstract

The asymptotic behavior of eigenvalues and eigenfunctions of $p$-Laplace operator is investigated. We obtain (I) the best constant of $L^\infty$-Poincaré's inequality, and (II) a limit equation which the limits of eigenvalues and eigenfunctions satisfy in a weak sense.

#### Article information

Source
Differential Integral Equations, Volume 12, Number 2 (1999), 183-206.

Dates
First available in Project Euclid: 29 April 2013

Fukagai, Nobuyoshi; Ito, Masayuki; Narukawa, Kimiaki. Limit as $p\to\infty$ of $p$-Laplace eigenvalue problems and $L^\infty$-inequality of the Poincaré type. Differential Integral Equations 12 (1999), no. 2, 183--206. https://projecteuclid.org/euclid.die/1367265629