On multiplicity of eigenvalues and symmetry of eigenfunctions of the $p$-Laplacian

@article{Audoux2018OnMO,
  title={On multiplicity of eigenvalues and symmetry of eigenfunctions of the \$p\$-Laplacian},
  author={Benjamin Audoux and Vladimir Bobkov and Enea Parini},
  journal={Topological Methods in Nonlinear Analysis},
  year={2018},
  volume={51},
  pages={565-582}
}
We investigate multiplicity and symmetry properties of higher eigenvalues and eigenfunctions of the p-Laplacian under homogeneous Dirichlet boundary conditions on certain symmetric domains Ω ⊂ R^N. By means of topological arguments, we show how symmetries of Ω help to construct subsets of W_0^(1,p)(Ω) with suitably high Krasnosel'ski˘ i genus. In particular, if Ω is a ball B ⊂ R^N , we obtain the following chain of inequalities: λ_2(p; B) ≤ · · · ≤ λ_(N+1)(p; B) ≤ λ_eq(p; B). Here λ_i(p; B) are… 

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