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Characterization of Two-Scale Gradient Young Measures and Application to Homogenization

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Abstract

This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures.

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Authors and Affiliations

  1. SISSA, Via Beirut 2-4, 34014, Trieste, Italy

    Jean-François Babadjian

  2. Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Margarida Baía & Pedro M. Santos

Authors
  1. Jean-François Babadjian
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  2. Margarida Baía
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  3. Pedro M. Santos
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Correspondence to Jean-François Babadjian.

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Correspondence to: Jean-François Babadjian.

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Babadjian, JF., Baía, M. & Santos, P.M. Characterization of Two-Scale Gradient Young Measures and Application to Homogenization. Appl Math Optim 57, 69–97 (2008). https://doi.org/10.1007/s00245-007-9012-y

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  • DOI: https://doi.org/10.1007/s00245-007-9012-y

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