Abstract
We discuss the problem of the global W 12 -regularity for the stress tensor of a perfect elastic-plastic body at equilibrium. In particular, we construct an example showing that the method proposed by the author to establish the local W 12 -regularity, in general, does not work in investigations of regularity up to the boundary if the given body is nonconvex. Bibliography: 3 titles.
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References
G. A. Seregin, “Differentiability of local extremals of variational problems in the mechanics of perfect elastoplastic media”,Differents. Uravn.,23, 1981–1991 (1987).
G. A. Seregin, “A local Caccioppoli-type estimate for extremals of variational problems in Hencky plasticity”, in:Some Applications of Functional Analysis to Problems of Mathematical Physics [in Russian], Novosibirsk (1988), pp. 127–138.
G. A. Seregin, “On regularity of weak solutions of variational problems in plasticity theory”,Algebra Analiz,2, 121–140 (1990).
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Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1996, pp. 227–232.
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Seregin, G.A. Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory. J Math Sci 93, 779–783 (1999). https://doi.org/10.1007/BF02366854
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DOI: https://doi.org/10.1007/BF02366854