The asymptotic behavior for divergence elliptic equations in exterior domains with periodic coefficients

TL;DR

This paper studies how solutions to divergence elliptic equations behave at infinity in exterior domains with periodic coefficients, extending known Liouville type results.

Contribution

It generalizes the Liouville type theorem for divergence elliptic equations in exterior domains with periodic coefficients.

Findings

Extended Liouville type result to broader class of equations

Characterized asymptotic behavior of solutions at infinity

Provided new insights into periodic coefficient effects

Abstract

In this paper, we investigate the asymptotic behavior of solutions for divergence linear elliptic equations in exterior domains with periodic coefficients. Consequently, we generalise the Liouville type result firstly established by Avellaneda and Lin.