Abstract
Linearly elastic laminates are examples of materials whose equilibrium equations may have only bounded measurable coefficients, yet whose solutions may be fairly smooth. This is quite different from general experience, where regularity of solutions is determined by the closeness of the system to a diagonal one. A particular situation where a laminate may appear is a highly twinned elastic or ferroelectric crystal, and there are questions related to these materials which make it useful to know some properties of these special systems of equations.
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References
A. Bensoussan, J.-L. Lions, & G. Papanicolaou, Asymptotic analysis for periodic structures, North Holland, (1978).
J. L. Ericksen, Ill posed problems in thermoelasticity theory, Systems of nonlinear partial differential equations, J. BALL (ed), Reidel, (1983), 71–93.
J. L. Ericksen, Twinning in crystals, I.M.A. preprint 95, (1984).
I. Fonseca, Variational methods for elastic crystals, Thesis, Univ. of Minnesota, (1985).
M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton, (1983).
D. Gilbarg & N. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, (1984).
D. Kinderlehrer, Twinning in crystals II, I.M.A. preprint 106, (1984).
D. Kinderlehrer & G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, (1980).
J.-L. Lions, Problèmes aux limites dans les équations aux dérivées partielles, Presse Université de Montréal, (1962).
W. H. Mcconnell, On the approximation of elliptic operators with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa, (1976), 121–137.
N. G. Meyers, An LP estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa, 17 (1963), 189–206.
N. G. Meyers & A. Elcrat, Some results on regularity for solutions of nonlinear elliptic systems and quasi-regular functions, Duke Math. J., 42 (1975), 121–136.
F. Murat, Compacité par compensation, Ann. Scuola Norm. Sup. Pisa, (1978), 489–507.
P. Podio-Guidugli, G. Vergara Caffarelli, & E. Virga, The role of ellipticity and normality assumptions in formulating live boundary conditions in elasticity, to appear Quart. Appl. Math.
L. Tartar, Compensated compactness and applications to partial differential equations, Nonlinear analysis and mechanics: Heriot-Watt symposium, R. J. Knops (ed), Research notes in math. 39, Pitman, (1979), 136–212.
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Dedicated to James Serrin on his sixtieth birthday
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© 1989 Springer-Verlag Berlin Heidelberg
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Chipot, M., Kinderlehrer, D., Caffarelli, G.V. (1989). Smoothness of Linear Laminates. In: Analysis and Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83743-2_19
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DOI: https://doi.org/10.1007/978-3-642-83743-2_19
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