Abstract:
We discuss the problem of global W12-regularity for the strew tensor of a perfect elastic-plastic body being in equilibrium. In particular, we construct an example, showing that the method proposed by the author to establish local W12-regularity, in general does not work in investigations of regularity up to the boundary if the given body is non-convex. Bibl. 3 titles.
Citation:
G. A. Seregin, “Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory”, Boundary-value problems of mathematical physics and related problems of function theory. Part 27, Zap. Nauchn. Sem. POMI, 233, POMI, St. Petersburg, 1996, 227–232; J. Math. Sci. (New York), 93:5 (1999), 779–783
\Bibitem{Ser96}
\by G.~A.~Seregin
\paper Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 1996
\vol 233
\pages 227--232
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3670}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1699125}
\zmath{https://zbmath.org/?q=an:0954.74508}
\transl
\jour J. Math. Sci. (New York)
\yr 1999
\vol 93
\issue 5
\pages 779--783
\crossref{https://doi.org/10.1007/BF02366854}
Linking options:
https://www.mathnet.ru/eng/znsl3670
https://www.mathnet.ru/eng/znsl/v233/p227
This publication is cited in the following 11 articles:
Arrigo Cellina, “On the regularity of solutions to the plastoelasticity problem”, Advances in Calculus of Variations, 13:1 (2020), 1
Bulicek M., Frehse J., “A Revision of Results For Standard Models in Elasto-Perfect-Plasticity Theory”, Calc. Var. Partial Differ. Equ., 57:2 (2018), 50
Knees D., “On Global Spatial Regularity and Convergence Rates for Time-Dependent Elasto-Plasticity”, Mathematical Models & Methods in Applied Sciences, 20:10 (2010), 1823–1858
P. Gruber, D. Knees, S. Nesenenko, M. Thomas, “Analytical and numerical aspects of time‐dependent models with internal variables”, Z Angew Math Mech, 90:10-11 (2010), 861
Demyanov A., “Quasistatic evolution in the theory of perfect elasto-plastic plates. Part II: Regularity of bending moments”, Ann Inst H Poincaré Anal Non Linéaire, 26:6 (2009), 2137–2163
Alber H.-D., Nesenenko S., “Local H-1-regularity and H1/3-delta-regularity up to the boundary in time dependent viscoplasticity”, Asymptot Anal, 63:3 (2009), 151–187
Demyanov A., “Regularity of stresses in Prandtl-Reuss perfect plasticity”, Calc Var Partial Differential Equations, 34:1 (2009), 23–72
Alber H.-D., Nesenenko S., “Local and Global Regularity in Time Dependent Viscoplasticity”, Iutam Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media, Iutam Bookseries, 11, 2008, 363–372
Knees D., “Global stress regularity of convex and some nonconvex variational problems”, Ann Mat Pura Appl, 187:1 (2008), 157–184
Knees D., “Global regularity of the elastic fields of a power-law model on Lipschitz domains”, Math Methods Appl Sci, 29:12 (2006), 1363–1391
Frehse J., Malek J., “Boundary Regularity Results for Models of Elasto-Perfect Plasticity”, Math. Models Meth. Appl. Sci., 9:9 (1999), 1307–1321
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