The author considers Naghdi's equations for a linearly elastic shell, clamped along its entire boundary, and proves that these equations are amenable to the theory of Agmon, Douglis, and Nirenberg. This allows the author to prove a regularity result for the corresponding weak solution.
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References
1.
[1] Bernadou, M. and Boisserie, J. M.: The Finite Element Method in Thin Shell Theory: Application to Arch Dam Simulation, Birhiuser, Boston, 1982.
2.
[2] Ciarlet, P. G.: The Finite Element Methodfor Elliptic Problems, North-Holland, Amsterdam, 1978.
3.
[3] Naghdi, P. M.: Foundations of elastic shells theory, in Progress in Solid Mechanics, vol. 4, pp. 1-90, North-Holland, Amsterdam, 1963.
4.
[4] Naghdi, P. M.: The theory of shells and plates, in Handbuch der Physik, vol. 6 a-2, pp. 425-640, Springer-Verlag, Berlin, 1972.
5.
[5] Cosserat, E. and Cosserat, F.: Thiorie des corps deformables, Hermann, Paris, 1909.
6.
[6] BabuAka, I., d'Harcourt, J. M., and Schwab, C.: Optimal shear correction factors in hierachic plate modelling, Math. Modelling and Sc. Computing, 1, 1-30 (1991).
7.
[7] Babuska, I. and Li, L.: The problem of plate modelling: Theoretical and computational results. Comput. Meth. Appl. Mech. Engig., 100, 249-273 (1992).
8.
[8] Schwab, C.: The Dimensional Reduction Method. Ph.D. Thesis, University of Maryland, College Park, 1989.
9.
[9] Agmon, S., Douglis, A., and Nirenberg, L.: Estimates near the boundary for solution of elliptic partial differential equations satisfying general boundary conditions II. Comm. Pure Appl. Math., 17, 35-92 (1964).
10.
[10] Bernadou, M., Ciarlet, P. G., and Miara, B.: Existence theorems for two-dimensional linear shell theories. J. Elasticity, 34(2), 111-138 (1994).
11.
[11] Necas, J.: Les methodes directes en thgorie des equations elliptiques, Masson, Paris, 1967.
12.
[12] Geymonat, G.: Sui problemi ai limiti per i sistemi lineari ellitici. Ann. Mat. Pura Appl., 69, 207-284 (1965).
[17] Alexandrescu-Iosifescu, 0.: Modeles de coques non liniaires: Existence et regularity. Doctoral Dissertation, Universite Pierre et Marie Curie, 1995.
