Calculus of Variations and Geometric Measure Theory
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L. Brasco - G. Franzina

A pathological example in Nonlinear Spectral Theory

created by brasco on 24 Feb 2017
modified on 08 Mar 2017



Inserted: 24 feb 2017
Last Updated: 8 mar 2017

Pages: 9
Year: 2017

We construct an open set $\Omega\subset\mathbb{R}^N$ on which an eigenvalue problem for the $p-$Laplacian has not isolated first eigenvalue and the spectrum is not discrete. The same example shows that the usual Lusternik-Schnirelmann minimax construction does not exhaust the whole spectrum of this eigenvalue problem.

Keywords: p-Laplacian, Nonlinear eigenvalue problems, Lusternik-Schnirelmann theory


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