Abstract:
The present work gives explicit criteria for the local continuity of the stress tensor, which is a minimizer of a two-dimensional variational problem (the Haar–Karman principle). The local continuity of the deformation tensor is derived from the dual relations that reflect the fact that the displacement vector and the stress tensor are the saddle point of a particular Lagrangian.
\Bibitem{Ser96}
\by G.~A.~Seregin
\paper Two-dimensional variational problems of the theory of plasticity
\jour Izv. Math.
\yr 1996
\vol 60
\issue 1
\pages 179--216
\mathnet{http://mi.mathnet.ru/eng/im67}
\crossref{https://doi.org/10.1070/IM1996v060n01ABEH000067}
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\zmath{https://zbmath.org/?q=an:0881.73039}
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https://doi.org/10.1070/IM1996v060n01ABEH000067
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This publication is cited in the following 15 articles:
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Miroslav Bulíček, Jens Frehse, “A revision of results for standard models in elasto-perfect-plasticity theory”, Calc. Var., 57:2 (2018)
Lisa Beck, Thomas Schmidt, “Convex duality and uniqueness for BV-minimizers”, Journal of Functional Analysis, 268:10 (2015), 3061
J. Math. Sci. (N. Y.), 178:3 (2011), 367–372
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Demyanov, A, “Quasistatic evolution in the theory of perfect elasto-plastic plates. Part II: Regularity of bending moments”, Annales de l Institut Henri Poincare-Analyse Non Lineaire, 26:6 (2009), 2137
M. Bulíček, J. Frehse, J. Málek, “On boundary regularity for the stress in problems of linearized elasto-plasticity”, Int J Adv Eng Sci Appl Math, 1:4 (2009), 141
Bildhauer M., Fuchs M., “Regularization of convex variational problems with applications to generalized Newtonian fluids”, Archiv der Mathematik, 84:2 (2005), 155–170
Bildhauer M., “Convex variational problems - Linear, nearly linear and anisotropic growth conditions”, Convex Variational Problems: Linear, Nearly Linear and Anisotropic Growth Conditions, Lecture Notes in Mathematics, 1818, 2003, 1–+
Bildhauer M., “A note on degenerate variational problems with linear growth”, Zeitschrift fur Analysis und Ihre Anwendungen, 20:3 (2001), 589–598
Fuchs M., Seregin G., “Variational methods for problems from plasticity theory and for generalized Newtonian fluids”, Variational Methods for Problems From Plasticity Theory and for Generalized Newtonian Fluids, Lecture Notes in Mathematics, 1749, 2000, 1–267
M. K. Renesse, “A counterexample to Hencky plasticity in the case of a thin plate under vertical load”, J Math Sci, 97:4 (1999), 4306
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