A mixed eigenvalue problem on domains tending to infinity in several directions

2025/10/31 by Prosenjit Roy, Roy, Prosenjit, Itai Shafrir +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2510.27455

Abstract

The aim of this article is to analyze the asymptotic behaviour of the eigenvalues of elliptic operators in divergence form with mixed boundary type conditions for domains that become unbounded in several directions, while they stay bounded in some directions (cylindrical domains). The limiting behavior of such eigenvalues is shown to depend on an ensemble of eigenvalue problems defined on a domain that is unbounded only in one direction. The asymptotic behavior of the eigenfunctions are also discussed. This work is a continuation of the work done in [6].

Citations

• Nonlinear elliptic eigenvalue problems in cylindrical domains becoming unbounded in one direction
• On some Variational Problems set on domains tending to infinity
• Asymptotics of eigenstates of elliptic problems with mixed boundary data on domains tending to infinity

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