Abstract
A lower semicontinuity theorem for integral functionals is proved underL 1-strong convergence of the trajectories andL 1-weak convergence of the control functions. An alternative statement is also proved under pointwise convergence of the trajectories.
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Olech, C.,Existence Theory in Optimal Control Problems--the Underlying Ideas, Proceedings of the International Conference on Differential Equations, Los Angeles, California, 1974, Academic Press, New York, New York, 1975.
Berkovitz, L. D.,Lower Semicontinuity of Integral Functionals, Transactions of the American Mathematical Society, Vol. 192, pp. 51–57, 1974.
Cesari, L.,Closure Theorems for Orientor Fields and Weak Convergence, Archive for Rational Mechanics and Analysis, Vol. 55, pp. 332–356, 1974.
Cesari, L.,Lower Semicontinuity and Lower Closure Theorems without Seminormality Condition, Annali di Matematica Pura e Applicata, Vol. 98, pp. 381–397, 1974.
Cesari, L.,A Necessary and Sufficient Condition for Lower Semicontinuity, Bulletin of the American Mathematical Society, Vol. 80, pp. 467–472, 1974.
Suryanarayana, M. B.,Remarks on Lower Semicontinuity and Lower Closure, Journal of Optimization Theory and Applications, Vol. 19, No. 1, 1976.
Cesari, L., andSuryanarayana, M. B.,Nemitsky's Operators and Lower Closure Theorems, Journal of Optimization Theory and Applications, Vol. 19, No. 1, 1976.
Poljak, B. T.,Semicontinuity of Integral Functionals and Existence Theorems for Extremal Problems (in Russian), Mathematiceskii Sbornik, Vol. 78, pp. 65–84, 1969.
Morozov, S. F., andPlotnikov, N. I.,On Necessary and Sufficient Conditions for Continuity and Semicontinuity of Functionals in Calculus of Variations, Matematiceskii Sbornik, Vol. 57, pp. 265–280, 1962.
Morrey, C. B.,Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, New York, 1966.
Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
Rockafellar, R. T.,Existence Theorems for General Control Problems of Bolza and Lagrange, Advances in Mathematics, Vol. 15, pp. 312–333, 1975.
Rockafellar, R. T.,Measurable Dependence of Convex Sets and Functions on Parameters, Journal of Mathematical Analysis and Applications, Vol. 28, pp. 4–25, 1969.
Olech, C.,The Characterization of the Weak Closure of Certain Sets of Integrable Functions, SIAM Journal on Control, Vol. 12, pp. 311–318, 1974.
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Olech, C. Weak lower semicontinuity of integral functionals. J Optim Theory Appl 19, 3–16 (1976). https://doi.org/10.1007/BF00934048
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DOI: https://doi.org/10.1007/BF00934048