New classes of integral functionals for which the integral representation of lower semicontinuous envelopes is valid
- Autores: Mandallena J.1, Sychev M.2,3
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Afiliações:
- Laboratoire MIPA, Site des Carmes
- Sobolev Institute of Mathematics, Siberian Branch
- Novosibirsk State University
- Edição: Volume 94, Nº 1 (2016)
- Páginas: 430-433
- Seção: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224049
- DOI: https://doi.org/10.1134/S1064562416040207
- ID: 224049
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Resumo
M.A. Sychev has recently shown that conditions necessary and sufficient for the lower semicontinuity of integral functionals with p-coercive integrands are W1,p-quasi-convexity and the so-called matching condition (M). Condition (M) is so general that there is the conjecture that is always holds in the case of continuous integrands. The paper develops relaxation theory (construction of lower semicontinuous envelopes) under the assumption that condition (M) holds. It turns out that, in this case, the theory has very good structure. Applications of general relaxation theory to particular cases, including the theory of strong materials, are also discussed.
Sobre autores
J.-Ph. Mandallena
Laboratoire MIPA, Site des Carmes
Email: masychev@math.nsc.ru
França, Place Gabriel Péri, Nîmes, 30021
M. Sychev
Sobolev Institute of Mathematics, Siberian Branch; Novosibirsk State University
Autor responsável pela correspondência
Email: masychev@math.nsc.ru
Rússia, pr. Akademika Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090