The ∞-eigenvalue problem with a sign-changing weight

Let Ω ⊂ R n be a smooth bounded domain and m ∈ C ( Ω ¯ ) be a sign-changing weight function. For 1 < p < ∞ , consider the eigenvalue problem - Δ p u = λ m ( x ) | u | p - 2 u in Ω , u = 0 on ∂ Ω , where Δ p u is the usual p -Laplacian. Our purpose in this article is to study the limit as p → ∞...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear differential equations and applications 2019-04, Vol.26 (2), p.1-20
Main Authors: Kaufmann, Uriel, Rossi, Julio D., Terra, Joana
Format: Article
Language:English
Subjects:
Analysis
Eigenvalues
Eigenvectors
Mathematics
Mathematics and Statistics
Weighting functions
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let Ω ⊂ R n be a smooth bounded domain and m ∈ C ( Ω ¯ ) be a sign-changing weight function. For 1 < p < ∞ , consider the eigenvalue problem - Δ p u = λ m ( x ) | u | p - 2 u in Ω , u = 0 on ∂ Ω , where Δ p u is the usual p -Laplacian. Our purpose in this article is to study the limit as p → ∞ for the eigenvalues λ k , p m of the aforementioned problem. In addition, we describe the limit of some normalized associated eigenfunctions when k = 1 .
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-019-0561-y