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Necessary conditions for nonconvex distributed control problems governed by elliptic variational inequalities. (English) Zbl 0471.49020


MSC:

49K99 Optimality conditions
49J40 Variational inequalities
35J20 Variational methods for second-order elliptic equations
54C08 Weak and generalized continuity
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
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[1] Barbu, V.; Precupanu, Th: Convexity and optimization in Banach spaces. (1978) · Zbl 0379.49010
[2] Brezis, H.: Problemes unilateraux. J. math. Pures appl. 51, 1-164 (1972)
[3] Brezis, H.; Strauss, W.: Semilinear second order elliptic equations in L1. J. math. Soc. Japan 25, 565-590 (1973) · Zbl 0278.35041
[4] Clarke, F. H.: Generalized gradients and applications. Trans. amer. Math. soc. 205, 247-262 (1975) · Zbl 0307.26012
[5] Duvaut, G.; Lions, J. L.: Inequalities in mechanics and physics. (1976) · Zbl 0331.35002
[6] Lions, J. L.: Optimal control of systems governed by partial differential systems. (1971) · Zbl 0203.09001
[7] Lions, J. L.: Various topics in the theory of optimal control of distributed systems. Lecture notes in economics and mathematical systems 105 (1974) · Zbl 0332.49001
[8] Lions, J. L.; Magenes, E.: Non homogeneous boundary value problems and applications. (1972) · Zbl 0223.35039
[9] Mignot, F.: Contrôle dans LES inéquations variationelles elliptiques. J. functional analysis 22, 130-185 (1976) · Zbl 0364.49003
[10] Necas, J.: LES méthodes directes dans la théorie des équations elliptiques. (1967)
[11] Rockafellar, R. T.: Integrals which are convex functionals. Pacific J. Math. 24, 525-539 (1968) · Zbl 0159.43804
[12] Rockafellar, R. T.: Conjugate convex functions in optimal control and the calculus of variations. J. math. Anal. appl. 32, 174-222 (1970) · Zbl 0218.49004
[13] Rockafellar, R. T.: Convex analysis. (1970) · Zbl 0193.18401
[14] Rockafellar, R. T.: La théorie des sousgradients et ses applications a l’optimization. (1978)
[15] Yosida, K.: Functional analysis. (1965) · Zbl 0126.11504
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