Journal of Mathematical Sciences

, Volume 99, Issue 1, pp 969–988 | Cite as

Regularity for minimizers of some variational problems in plasticity theory

  • G. A. Seregin
  • T. N. Shilkin


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.


Variational Problem Strain Tensor Local Coordinate System Plasticity Theory Duality Relation 
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  1. 1.
    G. A. Seregin, “On regularity of minimizers of some variational problems in plasticity theory”,Algebra Analiz,4, 181–218 (1993).Google Scholar
  2. 2.
    J. Frehse and G. A. Seregin, “Regularity for solutions of variational problems in the deformation theory of plasticity with logarithmic hardering”, Preprint421, Sfb256, Bonn (1995).Google Scholar
  3. 3.
    G. A. Seregin, “Differentiability properties of weak solutions for certain variational problems in the theory of perfect elastoplastic plates”,Appl. Math. Optim.,28, 307–335 (1993).MATHCrossRefGoogle Scholar
  4. 4.
    O. A. Ladyzhenskaya and N. N. Uraltseva,Linear and Quasilinear Equation of Elliptic Type [in Russian], Moscow (1973).Google Scholar
  5. 5.
    P. P. Mosolov and V. P. Myasnikov, “On correctness of boundary-value problems in mechanics of solids”,Math. Sb.,88, 256–287 (1972).Google Scholar
  6. 6.
    J. Frehse, “Two-dimensional variational problems with thin obstacles”,Math. Z.,143, 279–288 (1975).MATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • G. A. Seregin
  • T. N. Shilkin

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