Generalized eigenvalue problem for an interface elliptic equation

TL;DR

This paper studies a generalized eigenvalue problem for interface elliptic equations, characterizing principal eigenvalues and applying the results to population dynamics involving species interactions across geographical barriers.

Contribution

It introduces a novel characterization of principal eigenvalues for interface elliptic equations and applies it to ecological models with species interactions at borders.

Findings

Principal eigenvalues form a level set of a concave, regular function.

Application to population dynamics models with species interaction across barriers.

Provides a mathematical framework for ecological interface problems.

Abstract

In this paper we deal with an eigenvalue problem in an interface elliptic equation. We characterize the set of principal eigenvalues as a level set of a concave and regular function. As application, we study a problem arising in population dynamics. In these problems each species lives in a subdomain, and they interact in a common border, which acts as a geographical barrier.