Skip to main content
Log in

Necessary conditions for optimality in problems of control by systems described by elliptic equations

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. 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).

    Google Scholar 

  2. A. I. Egorov, “A variational problem in the theory of elliptic equations,” Sib. Mat. Zh.,5, No. 3, 500–508 (1964).

    Google Scholar 

  3. 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).

    Google Scholar 

  4. U. E. Raitum, “Some extremal problems connected with linear elliptic equations,” Latv. Mat. Ezhegodnik,4, 257–279 (1968).

    Google Scholar 

  5. 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).

    Google Scholar 

  6. T. Zolezzi, “Necessary conditions for optimal controls of elliptic or parabolic problems,” SIAM J. Control,10, No. 4, 594–607 (1972).

    Google Scholar 

  7. V. N. Gorchakov, “A problem in optimal control of a system described by an elliptic differential equation,” Kibernetika, No. 3, 101–103 (1974).

    Google Scholar 

  8. 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).

    Google Scholar 

  9. O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).

  10. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966).

  11. G. I. Marchuk, Methods in Computational Mathematics [in Russian], Nauka, Novosibirsk (1973).

    Google Scholar 

  12. A. A. Samarskii and V. B. Andreev, Difference Methods for Elliptic Equations [in Russian], Nauka, Moscow (1976).

    Google Scholar 

Download references

Authors

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

Reprints 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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00969946

Keywords

Navigation