A periodic homogenization problem with defects rare at infinity

Abstract

<p style='text-indent:20px;'>We consider a homogenization problem for the diffusion equation <inline-formula><tex-math id="M1">\begin{document}$ -\operatorname{div}\left(a_{\varepsilon} \nabla u_{\varepsilon} \right) = f $\end{document}</tex-math></inline-formula> when the coefficient <inline-formula><tex-math id="M2">\begin{document}$ a_{\varepsilon} $\end{document}</tex-math></inline-formula> is a non-local perturbation of a periodic coefficient. The perturbation does not vanish but becomes rare at infinity in a sense made precise in the text. We prove the existence of a corrector, identify the homogenized limit and study the convergence rates of <inline-formula><tex-math id="M3">\begin{document}$ u_{\varepsilon} $\end{document}</tex-math></inline-formula> to its homogenized limit.</p>