The principal eigenvalue problem for a strongly anisotropic second-order elliptic operator

2023/11/20 by Nathanaël Boutillon, Boutillon, Nathanaël
Mathematics · #35B09 #35J15 (Primary) #35P15 (Secondary) #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2311.12232

openalex publication_date 2023/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of the principal eigenfunction and is shown with a representation of the principal eigenfunction as a quasi-stationary distribution. Subsequent results deal with the limit of the principal eigenvalue and are shown using Hamilton-Jacobi equations.

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