On a Steklov-Robin eigenvalue problem

2022/10/06 by Nunzia Gavitone, Gavitone, Nunzia, Rossano Sannipoli +1 · 2 citations
Computer Science · Mathematics · #35B40 #35J25 #35P15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2210.02918

openalex publication_date 2022/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study a Steklov-Robin eigenvalue problem for the Laplacian in annular domains. More precisely, we consider Ω=Ω₀ ∖ B_r, where B_r is the ball centered at the origin with radius r>0 and Ω₀⊂ℝⁿ, n≥ 2, is an open, bounded set with Lipschitz boundary, such that B_r⊂ Ω₀. We impose a Steklov condition on the outer boundary and a Robin condition involving a positive L^∞-function β(x) on the inner boundary. Then, we study the first eigenvalue σ_β(Ω) and its main properties. In particular, we investigate the behaviour of σ_β(Ω) when we let vary the L¹-norm of β and the radius of the inner ball. Furthermore, we study the asymptotic behaviour of the corresponding eigenfunctions when β is a positive parameter that goes to infinity.

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• Estimates for the first and second Steklov-Dirichlet eigenvalues
• Optimality and stability of the radial shapes for the Sobolev trace constant

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