S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow (1970); English transl.: Pergamon Press, Oxford (1964).
Google Scholar
S. Germain, Recherches sur la Théorie des Surfaces Élastiques, Courcier, Paris (1821).
Google Scholar
G. R. Kirchhoff, “Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe,” J. Reine Angew. Math.
40, 51–88 (1850); 56, 285–313 (1859).
D. Morgenstern, “Herleitung der Plattentheorie aus der dreidimensionallen Elastozit ätstheorie,” Arch. Ration. Mech. Anal.
4, 145–152 (1959).
MathSciNet
MATH
Article
Google Scholar
B. A. Shoikhet, “On asymptotically exact equations of thin plates of complex structure” [in Russian], Prikl. Mat. Mekh.
37, 914–924 (1973); English transl.: J. Appl. Math. Mech.
37, 867–877 (1974).
MathSciNet
Article
Google Scholar
P. G. Ciarlet and P. Destuynder, “A justification of the two-dimensional plate model,” J. Mec. Paris
18, 315–344 (1979).
MathSciNet
MATH
Google Scholar
S. A. Nazarov, “Asymptotic analysis of an arbitrary anisotropic plate of variable thickness (a shallow shell)” [in Russian], Mat. Sb.
191, No 7, 129–159 (2000); English transl.: Sb. Math.
191, No. 7–8, 1075–1106 (2000).
MathSciNet
MATH
Article
Google Scholar
D. Percivale and P. Podio-Guidugli, “A general linear theory of elastic plates and its variational validation,” Boll. Unione Mat. Ital. (9)
2, No. 2, 321–341 (2009).
MathSciNet
MATH
Google Scholar
P. G. Ciarlet, Mathematical Elasticity, II: Theory of Plates, North-Holland, Amsterdam (1997).
Google Scholar
P. Destuynder, Une Théorie Asymptotique des Plaques Minces en Elasticité Linéaire, Masson, Paris (1986).
MATH
Google Scholar
S. A. Nazarov, Asymptotic Theory of Thin Plates and Rods. 1. Dimension Reduction and Integral Estimates [in Russian], Nauchnaya Kniga (IDMI), Novosibirsk (2002).
Google Scholar
O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973); English transl.: Springer, New York etc. (1985).
Google Scholar
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. I, Springer, Berlin etc. (1972).
Google Scholar
V. A. Kondrat’ev, “Boundary value problems for elliptic equations in domains with conical and angular points” [in Russian], Tr. Mosk. Mat. O-va
16, 219–292 (1963); English transl.: Trans. Moscow Math. Soc.
16, 227–313 (1967).
MATH
Google Scholar
S. A. Nazarov and B. A. Plamenevskii, Elliptic Problems in Domains with Piecewise Smooth Boundaries [in Russian], Nauka, Moscow (1991); English transl.: Walter de Gruyter, Berlin etc. (1994).
Book
Google Scholar
V. A. Kozlov, V. G, Maz’ya, J. Rossmann, Elliptic Boundary Value Problems in Domains with Point Singularities Am. Math. Soc., Providence, RI (1997).
MATH
Google Scholar
W. G. Maz’ya, S. A., Nazarov, B. A. Plamenevskii, Asymptotische Theorie Elliptischer Randwertaufgaben in Singulär Gestörten Gebieten. I [in German], Akademie-Verlag, Berlin (1991); English transl.: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. I, Birkhäuser, Basel (2000).
Google Scholar
G. Buttazzo and S. A. Nazarov, “Optimal location of support points in the Kirchhoff plate,” In: Proceedings of the Meeting “Variational Analysis and Aerospace Engineering II”. Erice 2010, Springer. [To appear]
G. Buttazzo, E. Oudet, and E. Stepanov, “Optimal transportation problems with free Dirichlet regions,” In: Variational Methods for Discontinuous Structures. Cernobbio 2001, pp. 41–65, Birkhäuser, Basel (2002).
Google Scholar
G. Bouchitté, C. Jimenez, and R. Mahadevan, “Asymptotic analysis of a class of optimal location problems,” J. Math. Pures Appl. (9)
95 (4) 382–419 (2011).
MathSciNet
MATH
Google Scholar
G. Buttazzo, F. Santambrogio, and N. Varchon, “Asymptotics of an optimal compliancelocation problem,” ESAIM Control Optim. Calc. Var.
12, 752–769 (2006).
MathSciNet
MATH
Article
Google Scholar
V. G. Maz’ya and B. A. Plamenevskii, “Estimates in L
p
and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary” Math. Nachr.
77, 25–82 (1977).
Google Scholar
A. M. Il’in, Matching of Asymptotic Expansions of Solutions of Boundary Value Problems [in Russian], Nauka, Moscow (1989); English transl.: Am. Math. Soc., Providence, RI (1992).
Google Scholar