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Lower semicontinuity of integral functionals. (English) Zbl 0294.49001


MSC:

49J10 Existence theories for free problems in two or more independent variables
49J20 Existence theories for optimal control problems involving partial differential equations
49J99 Existence theories in calculus of variations and optimal control
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[1] Leonard D. Berkovitz, Existence theorems in problems of optimal control, Studia Math. 44 (1972), 275 – 285. (errata insert). Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, III. · Zbl 0215.21406
[2] Leonard D. Berkovitz, Existence and lower closure theorems for abstract control problems, SIAM J. Control 12 (1974), 27 – 42. · Zbl 0243.93012
[3] Felix E. Browder, Remarks on the direct method of the calculus of variations, Arch. Rational Mech. Anal. 20 (1965), 251 – 258. · Zbl 0135.32404
[4] Gaetano Fichera, Semicontinuity of multiple integrals in ordinary form, Arch. Rational Mech. Anal. 17 (1964), 339 – 352. · Zbl 0128.10003
[5] Интеграл\(^{\приме}\)ные операторы в пространствах суммируемых функций, Издат. ”Наука”, Мосцощ, 1966 (Руссиан). · Zbl 0145.39703
[6] J.-L. Lions, Optimal control of systems governed by partial differential equations., Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, Band 170, Springer-Verlag, New York-Berlin, 1971. · Zbl 0203.09001
[7] Charles B. Morrey Jr., Multiple integral problems in the calculus of variations and related topics, Univ. of California Publ. Math. (N. S.) 1 (1943), 1 – 130.
[8] V. I. Plotnikov, Theorems on the existence of optimizing functions for optimal systems with distributed parameters, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 689 – 711 (Russian).
[9] B. T. Poljak, Semicontinuity of integral functionals and existence theorems in extrumum problems, Mat. Sb. (N.S.) 78 (120) (1969), 65 – 84 (Russian).
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