Bulletin of the Australian Mathematical Society

Research Article

CONTINUITY OF THE VARIATIONAL EIGENVALUES OF THE p-LAPLACIAN WITH RESPECT TO p

ENEA PARINIa1

a1 Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931 Köln, Germany (email: eparini@math.uni-koeln.de)

Abstract

In this note it is shown that a result of Champion and De Pascale [‘Asymptotic behavior of nonlinear eigenvalue problems involving p-Laplacian type operators’, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 1179–1195] implies that the variational eigenvalues of the p-Laplacian are continuous with respect to p.

(Received January 19 2010)

(Online publication March 15 2011)

2010 Mathematics subject classification

  • primary 35P30; secondary 49J45;
  • 49R50

Keywords and phrases

  • nonlinear eigenvalues;
  • p-Laplacian

Footnotes

The author acknowledges partial support by the DFG—Deutsche Forschungsgemeinschaft.