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Solution of a Ball–Murat problem

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Abstract

A necessary and sufficient condition for the W 1, p-quasi-convexity of integrands to imply the lower semicontinuity of the corresponding integral functionals with respect to the weak convergence of sequences in W 1, p is obtained. It is shown that the absence of the Lavrent’ev phenomenon in minimization problems with linear boundary data is sufficient, under a minor technical assumption, for the lower semicontinuity of integral functionals with quasi-convex integrands.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

    M. A. Sychev

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    M. A. Sychev

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

Additional information

Original Russian Text © M.A. Sychev, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 4, pp. 411–414.

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Sychev, M.A. Solution of a Ball–Murat problem. Dokl. Math. 92, 727–730 (2015). https://doi.org/10.1134/S1064562415060253

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  • DOI: https://doi.org/10.1134/S1064562415060253

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