International Journal of Differential Equations (Jan 2010)

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

  • Enea Parini

DOI
https://doi.org/10.1155/2010/984671
Journal volume & issue
Vol. 2010

Abstract

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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.