Characterization of the multiscale limit associated with bounded sequences in BV

Rita Ferreira*, Irene Fonseca

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (SciVal)


The notion of two-scale convergence for sequences of Radon measures with finite total variation is generalized to the case of multiple periodic length scales of oscillations. The main result concerns the characterization of (n+ l)-scale limit pairs (u, U) of sequences {(u EL N M[ω]*M(ωℝ d*N) x M(Q;R dxN) whenever {u e} £>o is a bounded sequence in SV(O;R d). This characterization is useful in the study of the asymptotic behavior of periodically oscillating functionals with linear growth, defined in the space BV of functions of bounded variation and described by n ε N microscales, undertaken in [10].

Original languageEnglish (US)
Pages (from-to)403-452
Number of pages50
JournalJournal of Convex Analysis
Issue number2
StatePublished - 2012
Externally publishedYes


  • BV-valued measures
  • Multiscale convergence
  • Periodic homogenization

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)


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