Quasistatic evolution in the theory of perfect elasto-plastic plates. Part II : regularity of bending moments

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1. [1] Anzellotti G., On the extremal stress and displacement in Hencky plasticity, Duke Math. J.51 (1984) 133-147. Zbl0548.73022MR744291
2. [2] Bensoussan A., Frehse J., Asymptotic behaviour of the time-dependent Norton–Hoff law in plasticity theory and $H^1$ regularity, Comment. Math. Univ. Carolinae37 (2) (1996) 285-304. Zbl0851.35079MR1399003
3. [3] Dal Maso G., Demyanov A., DeSimone A., Quasistatic evolution problems for pressure-sensitive plastic materials, Milan J. Math.75 (2007) 117-134. Zbl1225.74016MR2371540
4. [4] Dal Maso G., DeSimone A., Mora M.G., Quasistatic evolution problems for linearly elastic-perfectly plastic materials, Arch. Ration. Mech. Anal.180 (2) (2006) 237-291. Zbl1093.74007MR2210910
5. [5] Demengel F., Compactness theorems for spaces of functions with bounded derivatives and applications to limit analysis problems in plasticity, Arch. Ration. Mech. Anal.105 (1989) 123-161. Zbl0669.73030MR968458
6. [6] Demyanov A., Regularity of solutions in Prandtl–Reuss perfect plasticity, Calc. Var34 (2009) 23-72. Zbl1149.74014MR2448309
7. [7] Demyanov A., Quasistatic evolution in the theory of perfectly elasto-plastic plates. Part I: existence of a weak solution, Math. Models Meth. Appl. Sci.19 (2) (2009) 229-256. Zbl1160.74031MR2498434
8. [8] Fuchs M., Seregin G.A., Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids, Springer-Verlag, Berlin, 2000. Zbl0964.76003MR1810507
9. [9] Knees D., Global regularity of the elastic fields of a power-law model on Lipschitz domains, Math. Meth. Appl. Sci29 (2006) 1363-1391. Zbl1191.74015MR2247307
10. [10] Mazya V., Sobolev Spaces, Springer-Verlag, 1985. Zbl0692.46023
11. [11] Mielke A., Analysis of energetic models for rate-independent materials, in: Beijing, 2002, Proceedings of the International Congress of Mathematicians, vol. III, Higher Ed. Press, Beijing, 2002, pp. 817-828. Zbl1018.74007MR1957582
12. [12] Murat F., Trombetti C., A chain rule formula for the composition of a vector-valued function by a piecewise smooth function, Boll. Un. Mat. Ital. Sez. B6 (3) (2003) 581-595. Zbl1179.46037MR2014820
13. [13] Seregin G.A., Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory, J. Math. Sci.93 (5) (1999) 779-783. Zbl0954.74508MR1699125
14. [14] Seregin G.A., Two-dimensional variational problems in plasticity theory, Izv. Math.60 (1) (1996) 179-216. Zbl0881.73039MR1391123
15. [15] Seregin G.A., On regularity of minimizers of certain variational problems in plasticity theory, St. Petersburg Math. J.4 (1993) 1257-1272. Zbl0838.73029MR1202731
16. [16] Seregin G.A., Diferentiability properties of weak solutions of certain variational problems in the theory of perfect elastoplastic plates, Appl. Math. Optim.28 (1993) 307-335. Zbl0779.73086MR1227426
17. [17] Seregin G.A., On differentiability properties of the stress-tensor in the Coulomb–Mohr theory of plasticity, St. Petersburg Math. J.4 (6) (1993) 1257-1272. Zbl0838.73029MR1199642
18. [18] Seregin G.A., Differential properties of solution of evolution variational inequalities in the theory of plasticity, J. Math. Sci72 (6) (1994) 3449-3458. MR1317379
19. [19] Seregin G.A., Differentiability of local extremals of variational problems in the mechanics of perfect elastoplastic media, Differ. Uravn.23 (11) (1987) 1981-1991, (in Russian). English translation:, Differential Equations23 (1987) 1349-1358. Zbl0655.73017MR928247
20. [20] G.A. Seregin, Private communications. 
21. [21] Temam R., Mathematical Problems in Plasticity, Gauthier-Villars, Paris, 1985, Translation of, Problèmes mathématiques en plasticité, Gauthier-Villars, Paris, 1983. MR711964