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Regularity of solutions of nonlinear variational inequalities with a gradient bound as constraint. (English) Zbl 0338.49009

MSC:
49K27 Optimality conditions for problems in abstract spaces
35J60 Nonlinear elliptic equations
49K99 Optimality conditions
74C99 Plastic materials, materials of stress-rate and internal-variable type
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[1] Brezis, H, Multiplicateur de Lagrange en torsion elasto plastique. Arch. Rational Mech. Anal. 49, 32-40 (1972). · Zbl 0265.35021 · doi:10.1007/BF00281472
[2] Brezis, H, & M. Sibony, Equivalence de deux inéquations variationelles et applications. Arch. Rational Mech. Anal. 41, 254-265 (1971). · Zbl 0214.11104 · doi:10.1007/BF00250529
[3] Brezis, H., & G. Stampacchia, Sur la régularité de la solution d’inéquations elliptiques. Bull. Soc. Math. France 96, 153-180 (1968).
[4] Gerhardt, C., Regularity of solutions of nonlinear variational inequalities. Arch. Rational Mech. Anal. 52, 389-393 (1973). · Zbl 0277.49003 · doi:10.1007/BF00247471
[5] Hartmann, P., & G. Stampacchia, On some linear elliptic differential functional equations. Acta. Math. 115, 171-310 (1966). · Zbl 0142.38102 · doi:10.1007/BF02392210
[6] Lanchon, H., Torsion élastoplastique d’un arbre cylindrique de section simplement ou multiplement connexe. Thèse. Université de Paris VI (1972) · Zbl 0285.73020
[7] Stampacchia, G., Variational inequalities. Theory and Applications of Monotone Operators, pp. 101-192. A. Ghizzetti (ed.). Gubbio: Oderisi 1969.
[8] Ting, T.W., Elastic-plastic torsion of simply connected cylindrical bars. Indiana Univ. Math. Journal 20, 1047-1076 (1971). · Zbl 0214.24705 · doi:10.1512/iumj.1971.20.20100
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