Abstract
A variational problem for a functional depending on the symmetric part of the gradient of the unknown vectorvalued function is considered. We assume that the integrand of the problem has power growth with exponent less than two. We prove the existence of summable second derivatives near a flat piece of the boundary. In the two-dimensional case, Hölder continuity up to the boundary of the strain and stress tensors is established. Bibliography: 6 titles.
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References
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Dedicated to the memory of A. P. Oskolkov
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 243, 1997, pp. 270–298.
This research was supported by INTAS, grant No. 94-1375.
Translated by. I. A. Fedortsova.
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Seregin, G.A., Shilkin, T.N. Regularity for minimizers of some variational problems in plasticity theory. J Math Sci 99, 969–988 (2000). https://doi.org/10.1007/BF02673602
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DOI: https://doi.org/10.1007/BF02673602