Affiliations: Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85748 Garching bei München, Germany | Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, 38050 Povo (TN), Italy
Note: [] Corresponding author: Philipp Emanuel Stelzig, Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, 38050 Povo (TN), Italy. Tel.: +39 0461 283982; Fax: +39 0461 281624; E-mail: stelzig@ma.tum.de
Abstract: We study the effects of translation on two-scale convergence. Given a two-scale convergent sequence (uε(x))ε with two-scale limit u(x,y), then in general the translated sequence (uε(x+t))ε is no longer two-scale convergent, even though it remains two-scale convergent along suitable subsequences. We prove that any two-scale cluster point of the translated sequence is a translation of the original limit and has the form u(x+t,y+r) where the microscopic translation r belongs to a set that is determined solely by t and the vanishing sequence (ε). Finally, we apply this result to a novel homogenization problem that involves two different coordinate frames and yields a limiting behavior governed by emerging microscopic translations.
