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A direct proof for lower semicontinuity of polyconvex functionals

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Abstract

Lower semicontinuity for polyconvex functionals of the form ∫Ω g(detDu)dx with respect to sequences of functions fromW 1,n (Ω;ℝn) which converge inL 1 (Ωℝn) and are uniformly bounded inW 1,n−1 (Ω;ℝn), is proved. This was first established in [5] using results from [1] on Cartesian Currents. We give a simple direct proof which does not involve currents. We also show how the method extends to prove natural, essentially optimal, generalizations of these results.

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Authors and Affiliations

  1. Dipartimento di Matematica “R. Caccioppoli”, Universitá di Napoli, via Cintia, 80126, Napoli, Italy

    Nicola Fusco

  2. School of Mathematical Sciences, Australian National University, GPO Box 4, Canberra, ACT 0200, Australia

    John E. Hutchinson

Authors
  1. Nicola Fusco
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  2. John E. Hutchinson
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Supported by MURST, Gruppo Nazionale 40%

Partially supported by Australian Research Council

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Fusco, N., Hutchinson, J.E. A direct proof for lower semicontinuity of polyconvex functionals. Manuscripta Math 87, 35–50 (1995). https://doi.org/10.1007/BF02570460

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  • DOI: https://doi.org/10.1007/BF02570460

1991 Mathematics subject classification (Amer,. Math. Soc.)

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