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Title: Asymptotic behaviour of the time dependent Norton-Hoff law in plasticity theory and $H^{1}$ regularity (English)
Author: Bensoussan, A.
Author: Frehse, J.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 37
Issue: 2
Year: 1996
Pages: 285-304
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Category: math
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Summary: 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. (English)
Keyword: elasto-plasticity
Keyword: regularity
Keyword: variational inequalities
MSC: 35A15
MSC: 35D10
MSC: 35J45
MSC: 35J50
MSC: 35K65
MSC: 35K85
MSC: 35Q72
MSC: 73E50
idZBL: Zbl 0851.35079
idMR: MR1399003
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Date available: 2009-01-08T18:23:41Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/118833
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Reference: [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
Reference: [2] Duvaut G., Lions J.L.: Inequalities in Mechanics and Physics.Springer-Verlag Berlin (1976). Zbl 0331.35002, MR 0521262
Reference: [3] Lions J.L.: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod, Gauthier-Villars Paris (1969). Zbl 0189.40603, MR 0259693
Reference: [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.
Reference: [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.
Reference: [6] Seregin G.A.: Differentiability properties of the stress-tensor in perfect elastic-plastic theory.Preprint UTM321-Settembre Universita degli Studi di Trento, 1990.
Reference: [7] Le Tallec P.: Numerical Analysis of Viscoelastic problems.Masson Paris (1990). Zbl 0718.73091, MR 1071383
Reference: [8] Temam R.: Mathematical Problems in Plasticity.Gauthier Villars Paris (1985). MR 0711964
Reference: [9] Temam R.: A Generalized Norton-Hoff-Model and the Prandtl-Reuss-Law of Plasticity.Arch. Rat. Mech. Anal. 95 (1986), 137-181. Zbl 0615.73035, MR 0850094
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