Literature Cited
V. I. Plotnikov, “Necessary and sufficient conditions for optimality and uniqueness conditions for optimizing functions for general control systems,” Izv. Akad. Nauk SSSR, Ser. Mat.,36, No. 3, 652–679 (1972).
A. I. Egorov, “A variational problem in the theory of elliptic equations,” Sib. Mat. Zh.,5, No. 3, 500–508 (1964).
J. L. Lions, “Sur le contrôle optimal de systémes decrits per des équations aux dériveés partielles linéaires. Equations elliptiques,” Sci. C. R., Acad. Paris,263, No. 20, 713–715 (1966).
U. E. Raitum, “Some extremal problems connected with linear elliptic equations,” Latv. Mat. Ezhegodnik,4, 257–279 (1968).
E. I. Nenakhov and V. N. Gorchakov, “Necessary conditions on the extremum in problems of optimal control of systems described by elliptic equations in partial derivatives,” Kibernetika, No. 2, 77–80 (1972).
T. Zolezzi, “Necessary conditions for optimal controls of elliptic or parabolic problems,” SIAM J. Control,10, No. 4, 594–607 (1972).
V. N. Gorchakov, “A problem in optimal control of a system described by an elliptic differential equation,” Kibernetika, No. 3, 101–103 (1974).
I. K. Gogodze, “Necessary conditions for optimality in elliptic problems of control with integral bounds,” Soobshch. Akad. Nauk GSSR,81, No. 1, 17–20 (1976).
O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966).
G. I. Marchuk, Methods in Computational Mathematics [in Russian], Nauka, Novosibirsk (1973).
A. A. Samarskii and V. B. Andreev, Difference Methods for Elliptic Equations [in Russian], Nauka, Moscow (1976).
Additional information
Institute of Mechanics, Gorki State University. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 20, No. 3, pp. 586–596, May–June, 1979.
Rights and permissions
About this article
Cite this article
Kuznetsov, Y.A. Necessary conditions for optimality in problems of control by systems described by elliptic equations. Sib Math J 20, 410–417 (1979). https://doi.org/10.1007/BF00969946
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969946