The Second Eigenvalue of the p-Laplacian as p Goes to 1

International Journal of Differential Equations. 2010;2010 DOI 10.1155/2010/984671

 

Journal Homepage

Journal Title: International Journal of Differential Equations

ISSN: 1687-9643 (Print); 1687-9651 (Online)

Publisher: Hindawi Publishing Corporation

LCC Subject Category: Science: Mathematics

Country of publisher: Egypt

Language of fulltext: English

Full-text formats available: PDF, HTML, ePUB, XML

 

AUTHORS

Enea Parini (Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D 50931 Köln , Germany)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 20 weeks

 

Abstract | Full Text

The asymptotic behaviour of the second eigenvalue of the p-Laplacian operator as p goes to 1 is investigated. The limit setting depends only on the geometry of the domain. In the particular case of a planar disc, it is possible to show that the second eigenfunctions are nonradial if p is close enough to 1.