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The second eigenvalue of the p-Laplacian as p goes to 1

Parini, Enea (2010), The second eigenvalue of the p-Laplacian as p goes to 1, International Journal of Differential Equations, 2010. http://dx.doi.org/10.1155/2010/984671

Type
Article accepté pour publication ou publié
Date
2010
Journal name
International Journal of Differential Equations
Volume
2010
Publisher
Hindawi
Publication identifier
Metadata
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Author(s)
Parini, Enea
Abstract (EN)
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.
Subjects / Keywords
planar disc; p-Laplacian; eigenvalue