Remarks on the second Neumann eigenvalue

Date

2022-02-20

Authors

Sabina de Lis, Jose C.

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Publisher

Texas State University, Department of Mathematics

Abstract

This work reviews some basic features on the second (first nontrivial) eigenvalue λ2 to the Neumann problem -Δpu = λ|u|p-2u x ∈ Ω |∇u|p-2 ∂u/∂v = 0 x ∈ ∂Ω, where Ω is a bounded Lipschitz domain of ℝN, v is the outer unit normal, and ∆pu = div(|∇u|p-2∇u) is the p-Laplacian operator. We are mainly concerned with the variational characterization of λ2 and place emphasis on the range 1 < p < 2, where the nonlinearity |u|p-2u becomes non smooth. We also address the corresponding result for the p-Laplacian in graphs.

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Keywords

p-Laplacian operator, Eigenvalues, Neumann conditions

Citation

Sabina de Lis, J. C. (2022). Remarks on the second Neumann eigenvalue. <i>Electronic Journal of Differential Equations, 2022</i>(13), pp. 1-12.

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Attribution 4.0 International

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