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 Uspekhi Mat. Nauk, 1972, Volume 27, Issue 3(165), Pages 21–77 (Mi umn5057)

Convexity of values of vector integrals, theorems on measurable choice and variational problems

V. I. Arkin, V. L. Levin

Abstract: We give an account of applications of measurable many-valued mappings and theorems on convexity of finite-dimensional vector integrals to several variational problems. Theorems on convexity are carried over to vector integrals with values in function spaces, and with the help of these we obtain a aximum principle as a ecessary and sufficient extremum condition and an existence theorem for a on-linear variational problem with operator constraints of integral equality type, similar to Monge's problem on mass displacement.

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English version:
Russian Mathematical Surveys, 1972, 27:3, 21–85

Bibliographic databases:

UDC: 517.4+519.3+519.9
MSC: 28B05, 46G10, 26B25, 30C80, 47J20

Citation: V. I. Arkin, V. L. Levin, “Convexity of values of vector integrals, theorems on measurable choice and variational problems”, Uspekhi Mat. Nauk, 27:3(165) (1972), 21–77; Russian Math. Surveys, 27:3 (1972), 21–85

Citation in format AMSBIB
\Bibitem{ArkLev72} \by V.~I.~Arkin, V.~L.~Levin \paper Convexity of values of vector integrals, theorems on measurable choice and variational problems \jour Uspekhi Mat. Nauk \yr 1972 \vol 27 \issue 3(165) \pages 21--77 \mathnet{http://mi.mathnet.ru/umn5057} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=405097} \zmath{https://zbmath.org/?q=an:0254.49006} \transl \jour Russian Math. Surveys \yr 1972 \vol 27 \issue 3 \pages 21--85 \crossref{https://doi.org/10.1070/RM1972v027n03ABEH001378} 

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