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.
@article{118833,
author = {Alain Bensoussan and Jens Frehse},
title = {Asymptotic behaviour of the time dependent Norton-Hoff law in plasticity theory and $H^{1}$ regularity},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {37},
year = {1996},
pages = {285-304},
zbl = {0851.35079},
mrnumber = {1399003},
language = {en},
url = {http://dml.mathdoc.fr/item/118833}
}
Bensoussan, Alain; Frehse, Jens. Asymptotic behaviour of the time dependent Norton-Hoff law in plasticity theory and $H^{1}$ regularity. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 285-304. http://gdmltest.u-ga.fr/item/118833/
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). (1993) | MR 1260435
Inequalities in Mechanics and Physics, Springer-Verlag Berlin (1976). (1976) | MR 0521262 | Zbl 0331.35002
Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars Paris (1969). (1969) | MR 0259693 | Zbl 0189.40603
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. (1987)
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.
Differentiability properties of the stress-tensor in perfect elastic-plastic theory, Preprint UTM321-Settembre Universita degli Studi di Trento, 1990.
Numerical Analysis of Viscoelastic problems, Masson Paris (1990). (1990) | MR 1071383 | Zbl 0718.73091
Mathematical Problems in Plasticity, Gauthier Villars Paris (1985). (1985) | MR 0711964
A Generalized Norton-Hoff-Model and the Prandtl-Reuss-Law of Plasticity, Arch. Rat. Mech. Anal. 95 (1986), 137-181. (1986) | MR 0850094 | Zbl 0615.73035