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Lower semicontinuity of quasiconvex integrals

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Summary

New lower semicontinuity results for quasiconvex integrals. In particular, under certain structure conditions and growth 0≤F(ξ)≤C(∣≤∣q) the functional ∫ Ω F(∇u)dx is proved to be lower semicontinuous onW 1,q with respect to the weak convergence inW 1,p, p≥q−1.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18600, Praha 8, The Czech Republic

    Jan Malý

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  1. Jan Malý
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Research supported by the grant No. 201/93/2171 of Czech Grant Agency (GAČR) and by the grant No. 364 of Charles University (GAUK).

This article was processed by the author using the Springer-VerlagTex P Jourlg marco package 1991.

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Malý, J. Lower semicontinuity of quasiconvex integrals. Manuscripta Math 85, 419–428 (1994). https://doi.org/10.1007/BF02568208

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  • DOI: https://doi.org/10.1007/BF02568208

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