On the interplay of two-scale convergence and translation

Research output: Contribution to journalResearch articleContributedpeer-review


  • Stefan Neukamm - , Technical University of Munich (Author)
  • Philipp Emanuel Stelzig - , Technical University of Munich (Author)


We study the effects of translation on two-scale convergence. Given a two-scale convergent sequence (u epsilon(x))epsilon with two-scale limit u(x, y), then in general the translated sequence (u epsilon(x + t))epsilon 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 (epsilon). 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.


Original languageEnglish
Pages (from-to)163-183
Number of pages21
JournalAsymptotic analysis
Issue number3
Publication statusPublished - 2011
Externally publishedYes

External IDs

Scopus 79952797799



  • two-scale convergence, translation, homogenization, Gamma-convergence, BLOCH-WAVE HOMOGENIZATION, DOUBLE-POROSITY MODEL, INTEGRAL FUNCTIONALS, ASYMPTOTIC ANALYSIS, FLOW

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