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Abstrakty
We discuss the weak form of the Ramberg/Osgood equations (also known as the Norton/Hoff model) for nonlinear elastic materials on a 3-dimensional domain and show that the stress tensor is Hoelder continuous on an open subset whose complement is of Lebesguemeasure zero. We also give an estimate for the Hausdorff-dimension of the singular set.
Wydawca
Czasopismo
Rocznik
Tom
Strony
209--233
Opis fizyczny
Bibliogr. 14 poz.
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autor
autor
- Univeritaet des Saarlandes. Fachbercich 6.1 Mathematik, Postfach 15 11 50, D-66041 Saarbruecken, Germany, bibli@match.uni-sb.de
Bibliografia
- [1] Adams, R. A., Sobolev Spaces, Academic Press, New York-San Francisco-London, 1975.
- [2] Bensoussan, A., Frehse, .1., Asymptotic behaviour of Norton-Hoff's law in plasticity theory and H1 regularity, in: "Boundary Value Problems for Partial Differential Equations and Applications", Res. Notes Appl. Math. 29, Masson, Paris, 1993, 3 26.
- [3] Bildhauer. M., Fuchs, M., Smoothness of weak solutions of the Ramberg/Osgood equations on plane domains, Z. Angew. Math. Mech. 87 (2007), 70-76.
- [4] Bildhauer, M., Fuchs, M., Repin, S., A functional type a posteriori error analysis for the Ramberg-Osgood model, Z. Angew. Math. Mech, (to appear).
- [5] Bildhauer, M., Fuchs, M., Zhong, X., A lemma on the higher integrability of functions with applications to the regularity theory of two-dimensional generalized Newtonian fiuids, Manuscripta Math. 116 (2005), 135-156.
- [6] Fuchs, M., Li, G., Variational inequalities for energy functionals with nonstandard growth conditions, Abstr. Appl. Anal. 3(1-2) (1998), 41-64.
- [7] Fuchs, M., Seregin, G., Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids, Lecture Notes in Math. 1749, Springer, Berlin-Heidelberg, 2000.
- [8] Giaquinta, M., Multiple lntegrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. of Math. Stud. 105, Princeton University Press, Princeton, 1983.
- [9] Giaquinta, M., Modica, G., Nonlinear systems of the type of the stationary Navier-Stokes system, J. Reine Angew, Math. 330 (1982), 173-214,
- [10] Geymonat, G., Suquet, P., Functional spaces for Norton-Hoff materials, Math, Methods Appl. Sci. 8 (1986), 206-222,
- [11] Knees, D., Regularity results for quasilinear elliptic systems of power-law growth in nonsmooth domains boundary, transmission and crock problems, Dissertation. Fakultat Mathematik und Physik, Universitat Stuttgart, 2004.
- [12] Osgood, W. R., Ramberg, W., Description of stress-strain curves by three parameters, Tech. Notes Nat, Adv. Comm. Aeronaut. 1943(902) (1943), 13 pp. (15 plates),
- [13] Seregin, G., On the regularity of the minimizers of some ariational problems of plasticity theory, St. Petersburg Math. J. 4 (1993), 989-1020.
- [14] Temam, R., Mathematical Problems in Plasticity, Gauthier-Villars, Paris, 1985
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-LOD6-0002-0038