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Keywords:
control of variational inequalities; optimal design; minimization; pseudoplate with obstacles; cost functional; thickness; $G$-convergence; coercive variational inequality; approximate optimization problem; finite element
Summary:

References:
[1] Adams, R. A.: Sobolev Spaces. Academic Press New York-London (1975). MR 0450957 | Zbl 0314.46030
[2] Armand, J. L.: Application of the Theory of Optimal Control of Distributed Parameter Systems of Structural Optimization. NASA (1972).
[3] Boccardo, L., Murat, F.: Nouveaux résultats de convergence des problèmes unilateraux. Res. Notes Math. 60 (1982), 64-85 French. MR 0652507
[4] Boccardo, L., Marcellini, F.: Sulla convergenza delle soluzioni di disequazioni variazionali. Ann. Mat. Pura Appl., IV. Ser. 110 (1976), 137-159 Italian. MR 0425344 | Zbl 0333.35030
[5] Boccardo, L., Dolcetta, J. C.: $G$-convergenza e problema di Dirichlet unilaterale. Boll. Unione Math. Ital., IV. Ser. 12 (1975), 115-123 Italian. MR 0399988 | Zbl 0337.35023
[6] Brezis, H., Stampacchia, G.: Sur la régularité de la solution d'inéquations elliptiques. Bull. Soc. Math. Fr. 96 (1968), 153-180 French. MR 0239302 | Zbl 0165.45601
[7] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems. North Holland Amsterdam-New York-Oxford (1978). MR 0520174 | Zbl 0383.65058
[8] Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. Springer New York (1984). MR 0737005 | Zbl 0536.65054
[9] Haslinger, J., Mäkinen, R. A. E.: Introduction to Shape Optimization. Theory, Approximation and Computation Advance in Design and Control. SIAM Philadelphia (2003). MR 1969772
[10] Hlaváček, I., Chleboun, J., Babuška, I.: Uncertain Input Data Problems and the Worst Scenario Method. Elsevier Amsterdam (2004). MR 2285091 | Zbl 1116.74003
[11] Hlaváček, I., Lovíšek, J.: Control in obstacle-pseudoplate problems with friction on the boundary. Optimal design and problems with uncertain data. Applicationes Mathematicae 28 (2001), 407-426 Control in obstacle-pseudoplate problems with friction on the boundary. Approximate optimal design and worst scenario problems. Applicationes Mathematicae 29 (2002), 75-95. MR 1873903
[12] Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic Press New York (1980). MR 0567696 | Zbl 0457.35001
[13] Křížek, M., Neittaanmäki, P.: Finite Element Approximation of Variational Problems and Applications. Longman Scientific & Technical/John Wiley & Sons Harlow/New York (1990). MR 1066462
[14] Lurie, K. A., Cherkaev, A. V.: $G$-closure of a set of anisotropically conducting media in the two dimensional case. J. Optimization Theory Appl. 42 (1984), 283-304. MR 0737972 | Zbl 0504.73060
[15] Mignot, F.: Controle dans les inéquations variationelles elliptiques. J. Funct. Anal. 22 (1976), 130-185 French. MR 0423155 | Zbl 0364.49003
[16] Murat, F.: $H$-convergence. Séminaire d'Analyse Fonctionnelle et Numérique de l'Université d'Alger. Lecture Notes (1977-1978).
[17] Nečas, J.: Les Méthodes Directes en Théorie des Équations Elliptiques. Academia Prague (1967), French. MR 0227584
[18] Petersson, J.: On stiffness maximization of variable thickness sheet with unilateral contact. Q. Appl. Math. 54 (1996), 541-550. MR 1402408 | Zbl 0871.73046
[19] Raitum, U. E.: Sufficient conditions for sets of solutions of linear elliptic equations to be weakly sequentially closed. Latvian Math. J. 24 (1980), 142-155. MR 0616251
[20] Rodrigues, J.-F.: Obstacle Problems in Mathematical Physics. North Holland Amsterdam (1987). MR 0880369 | Zbl 0606.73017
[21] Shillor, M., Sofonea, M., Telega, J. J.: Models and Analysis of Quasistatic Contact. Variational Methods. Springer Berlin (2004). Zbl 1069.74001
[22] Sokolowski, J.: Optimal control in coefficients of boundary value problems with unilateral constraints. Bull. Pol. Acad. Sci., Tech. Sci. 31 (1983), 71-81. Zbl 0544.49005
[23] Spagnolo, S.: Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche. Ann. Sc. Norm. Super. Pisa Sci. Fis. Mat., III. Ser. 22 (1968), 571-597 Italian. MR 0240443
[24] Zhikov, V. V., Kozlov, S. M., Oleinik, O. A.: Homogenization of Differential Operators and Integral Functionals. Springer Berlin (1994). MR 1329546
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