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The theorem on convergence with a functional for integral functionals with p(x)- and p(x, u)-growth

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Abstract

We continue studying weak convergence for the integral functionals satisfying p(x)- and p(x, u)-growth conditions. We obtain the theorem on convergence with a functional and some results on the relation between integral functionals and their abstract lower semicontinuous extensions.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    M. A. Sychev

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  1. M. A. Sychev
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Correspondence to M. A. Sychev.

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Original Russian Text Copyright © 2012 Sychev M.A.

The author was supported by the Russian Foundation for Basic Research (Grant 12-01-00390), the Integration Grant of the Siberian Division of the Russian Academy of Sciences (No. 30) and the Presidium of the Russian Academy of Sciences (No. 15) The author’s approach to the theory of Young measures was developed during his stays at the ICTP-SISSA (Trieste, Italy) in 1995–1997. Subsequent work was done at the Mathematics Department of Carnegie Mellon University (Pittsburgh, USA) and the Max Planck Institute (Leipzig, Germany).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 931–942, July–August, 2012.

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Sychev, M.A. The theorem on convergence with a functional for integral functionals with p(x)- and p(x, u)-growth. Sib Math J 53, 748–756 (2012). https://doi.org/10.1134/S0037446612040167

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