On the optimal design of elastic shafts
ESAIM: Modélisation mathématique et analyse numérique, Tome 23 (1989) no. 4, pp. 615-625. 
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     author = {Gonzalez de Paz, Raul B.},
     title = {On the optimal design of elastic shafts},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {615--625},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {23},
     number = {4},
     year = {1989},
     mrnumber = {1025075},
     zbl = {0688.73063},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1989__23_4_615_0/}
}
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Gonzalez de Paz, Raul B. On the optimal design of elastic shafts. ESAIM: Modélisation mathématique et analyse numérique, Tome 23 (1989) no. 4, pp. 615-625. http://www.numdam.org/item/M2AN_1989__23_4_615_0/

[1] A. Acker, A free boundary optimization problem. SIAM J. Math. Anal. 9(1978) pp.1179-1191. | MR | Zbl

[2] H. W. Alt and L. A. Cafarelli, Existence and regularity for a minimum problem with free boundary. J. Reine u. Angew. Mathematik 325 (1981)pp. 104-144. | MR | Zbl

[3] N. V. Banichuk, Problems and methods of optimal structural design. Plenum Press, London (1983). | MR | Zbl

[4] N. Bourbaki, Espaces Vectoriels Topologiques, Hermann, Paris (1973).

[5] Ch. Castaing and M. Valadier, Convex Analysis and Measurable Multifonctions. Lect. Notes in Math. no. 580, Springer-Verlag, New York (1977). | MR | Zbl

[6] J. Cea, Optimisation, théorie et algorithmes. Dunod, Paris (1971). | MR | Zbl

[7] J. Cea, Problems of shape optimal design in « Optimization of distributed parameter structures, NATO Proceedings » (Eds. Haug, E. J. and Cea, J. ). Sijthoff and Noordhoff (1981). | Zbl

[8] J. Cea and K. Malanowski, An example of a max-min problem in partial differential equations. SIAM J. Control and Optimization (1970) pp. 305-316. | MR | Zbl

[9] D. Chenais, On the exixtence of a solution in a domain identification problem, J. Math. Anal. and Appl. 52 (1975) pp. 189-219. | MR | Zbl

[10] I. Ekeland and R. Temam, Analyse convexe et problèmes variationels. Dunod, Paris (1974). | MR | Zbl

[11] Cl. Gebhardt, Regularity of solutions of non-linear variational inequalities. Arch. Rat. Mech. and Anal. 52 (1973) pp. 383-393. | Zbl

[12] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Aquations of second order. Springer, New York (1977). | MR | Zbl

[13] R. B. Gonzalez De Paz, Sur un problème d'optimisation de domaine. Numer. Funct. Anal. and Optimiz. 5 (1982) pp. 173-197. | MR | Zbl

[14] B. Kawohl, Geometrical properties of level sets of solutions to elliptic problems. Proc. Symp. in Pure Math. A.M.S. (1986), part 2, pp. 25-36. | MR | Zbl

[15] D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Academic Press, New York (1980). | MR | Zbl

[16] H. Lanchon, Torsion élastoplastique d'un arbre. J. de Mech. 13 (1974) pp. 367-318. | MR

[17] J. J. Moreau, Fonctionnelles convexes. Séminaire sur les équations aux dérivées partielles. Collèges de France (1966-67). | Numdam

[18] J. Neças, Les méthodes directes en théorie des équations elliptiques. Masson, Paris (1967). | MR

[19] J. Pironneau, Optimal shape design for elliptic systems. Springer-Verlag, New York (1984). | MR | Zbl

[20] G. Polya and A. Weinstein, On the torsional rigidity of multiply-connected cross sections. Ann. Math. 52 (1950) pp. 154-163. | MR | Zbl

[21] M. Valadier, Sous-différentiels d'une borne supérieure et d'une somme continue de fonctions convexes. C. R. Acad. Sc. Paris, Serie A, 268, pp. 39-42 (janvier 1969). | MR | Zbl

[22] J. P. Zolesio, Domain variational formulation for free boundary problem, in « Optimization of distributed parameter structures. NATO-Proceedings » (Eds. Haug, E. J. and Cea. J.). Sijthoff and Noordhoff (1981). | MR | Zbl

[23] J. P. Zolesio, Indentification de domaines par déformation. Doctoral Thesis, Université de Nice (1979).

[24] R. Jensen, Boundary regularity for variational inequalities. Indiana Univ. Math. J. 29 (1980) pp. 495-511. | MR | Zbl