Abstract:
In this paper local properties of weak solutions of nonlinear elliptic systems arising in problems of the deformation theory of plasticity are investigated. Lp-estimates are obtained for a weak solution in the case of plasticity with power-type consolidation. For linear consolidation various properties are established, such as the Hölder continuity of a weak solution, the square-integrability of its second order derivatives, and Lp-estimates for these derivatives. Here the elasticity and plasticity domains are introduced. In the former the solution is regular, while in the latter, when there are more than two variables, a weak solution has Hölder continuous first derivatives in a subdomain that differs from the plasticity domain by a set of measure zero.
Bibliography: 20 titles.
Citation:
G. A. Seregin, “On differential properties of weak solutions of nonlinear elliptic systems arising in plasticity theory”, Math. USSR-Sb., 58:2 (1987), 289–309
\Bibitem{Ser86}
\by G.~A.~Seregin
\paper On differential properties of weak solutions of nonlinear elliptic systems arising in plasticity theory
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 2
\pages 289--309
\mathnet{http://mi.mathnet.ru/eng/sm1874}
\crossref{https://doi.org/10.1070/SM1987v058n02ABEH003105}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=865763}
\zmath{https://zbmath.org/?q=an:0709.73023}
Linking options:
https://www.mathnet.ru/eng/sm1874
https://doi.org/10.1070/SM1987v058n02ABEH003105
https://www.mathnet.ru/eng/sm/v172/i3/p291
This publication is cited in the following 4 articles:
Fuchs M., Repin S., “A Posteriori Error Estimates for the Approximations of the Stresses in the Hencky Plasticity Problem”, Numer. Funct. Anal. Optim., 32:6 (2011), 610–640
P. Gruber, D. Knees, S. Nesenenko, M. Thomas, “Analytical and numerical aspects of time-dependent models with internal variables”, Z angew Math Mech, 2010, n/a
J. Math. Sci. (N. Y.), 178:3 (2011), 367–372
Seregin G., “Differential Properties of the Extremals of Variational-Problems, Occurring in Plasticity Theory”, Differ. Equ., 26:6 (1990), 756–766
Citation in format AMSBIB
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