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A necessary and sufficient condition for lower semicontinuity. (English) Zbl 0287.49003

MSC:
49J27 Existence theories for problems in abstract spaces
49J45 Methods involving semicontinuity and convergence; relaxation
49J05 Existence theories for free problems in one independent variable
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[1] Lamberto Cesari, Existence theorems for multidimensional Lagrange problems, J. Optimization Theory Appl. 1 (1967), 87 – 112. · Zbl 0156.12503
[2] Lamberto Cesari, Lower semicontinuity and lower closure theorems without seminormality conditions, Ann. Mat. Pura Appl. (4) 98 (1974), 381 – 397. · Zbl 0281.49006
[3] Lamberto Cesari, Closure theorems for orientor fields, Bull. Amer. Math. Soc. 79 (1973), 684 – 689. · Zbl 0353.49034
[4] Lamberto Cesari, Closure theorems for orientor fields and weak convergence, Arch. Rational Mech. Anal. 55 (1974), 332 – 356. · Zbl 0296.49029
[5] L. Cesari and M. B. Suryanarayana, Closure theorems without seminormality conditions, J. Optimization Theory Appl. 15 (1975), 441 – 465. Existence theory in the calculus of variations and optimal control. · Zbl 0279.49010
[6] R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York-Toronto-London, 1965. · Zbl 0182.16101
[7] M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, Translated by A. H. Armstrong; translation edited by J. Burlak. A Pergamon Press Book, The Macmillan Co., New York, 1964.
[8] Charles B. Morrey Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966. · Zbl 0142.38701
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