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elasto-plasticity; regularity; variational inequalities
We prove $H^{1}_{\operatorname{loc}}$-regularity for the stresses in the Prandtl-Reuss-law. The proof runs via uniform estimates for the Norton-Hoff-approximation.
[1] Bensoussan A., Frehse J.: Asymptotic Behaviour of Norton-Hoff's Law in Plasticity theory and $H^{1}$ Regularity. Collection: Boundary Value Problems for Partial Differential Equations and Applications, RMA Res. Notes Appl. Math. (Vol. in honor of E. Magenes) Masson Paris 3-25 29 (1993). MR 1260435
[2] Duvaut G., Lions J.L.: Inequalities in Mechanics and Physics. Springer-Verlag Berlin (1976). MR 0521262 | Zbl 0331.35002
[3] Lions J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars Paris (1969). MR 0259693 | Zbl 0189.40603
[4] Seregin G.A.: Differentiabilty properties of the stress tensor in perfect elastic-plastic theory. Differentsial'nye Uravneniya 23 (1987), 1981-1991 English translation in Differential Equations 23 (1987), 1349-1358.
[5] Seregin G.A.: Differentiability of solutions of certain variational inequalities describing the quasi-static equilibrium of an elastic-plastic body. Pomi, Preprints E-1-92 Steklov Mathematical Institute Sankt Petersburg, 1992.
[6] Seregin G.A.: Differentiability properties of the stress-tensor in perfect elastic-plastic theory. Preprint UTM321-Settembre Universita degli Studi di Trento, 1990.
[7] Le Tallec P.: Numerical Analysis of Viscoelastic problems. Masson Paris (1990). MR 1071383 | Zbl 0718.73091
[8] Temam R.: Mathematical Problems in Plasticity. Gauthier Villars Paris (1985). MR 0711964
[9] Temam R.: A Generalized Norton-Hoff-Model and the Prandtl-Reuss-Law of Plasticity. Arch. Rat. Mech. Anal. 95 (1986), 137-181. MR 0850094 | Zbl 0615.73035
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