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Mat. Sb. (N.S.), 1977, Volume 102(144), Number 2, Pages 260–279 (Mi msb2682)  

This article is cited in 8 scientific papers (total in 8 papers)

On the Dirichlet problem for Bellman's equation in a plane domain

M. V. Safonov


Abstract: The Dirichlet problem for Bellman's equation in a plane domain is considered. It is shown that, under certain assumptions about the type of smoothness and the “weak” nondegeneracy of the corresponding controlled diffusion process, the solution of this Dirichlet problem is the pay-off function of an optimal control problem. Under supplementary assumptions about smoothness, the pay-off function is also smooth.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1977, 31:2, 231–248

Bibliographic databases:

UDC: 517.544+519.2
MSC: Primary 60H15, 35J60; Secondary 60J65, 35J25, 93E20
Received: 01.04.1976

Citation: M. V. Safonov, “On the Dirichlet problem for Bellman's equation in a plane domain”, Mat. Sb. (N.S.), 102(144):2 (1977), 260–279; Math. USSR-Sb., 31:2 (1977), 231–248

Citation in format AMSBIB
\Bibitem{Saf77}
\by M.~V.~Safonov
\paper On the Dirichlet problem for Bellman's equation in a~plane domain
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 102(144)
\issue 2
\pages 260--279
\mathnet{http://mi.mathnet.ru/msb2682}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=445110}
\zmath{https://zbmath.org/?q=an:0347.93050|0386.93059}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 31
\issue 2
\pages 231--248
\crossref{https://doi.org/10.1070/SM1977v031n02ABEH002300}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977FY72200007}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Safonov, “On the Dirichlet problem for Bellman's equation in a plane domain”, Math. USSR-Sb., 34:4 (1978), 521–526  mathnet  crossref  mathscinet  zmath
    2. Safonov M., “On Dirichlet Problem for the Bellman Equation in a Multidimensional Domain”, 253, no. 3, 1980, 535–540  mathscinet  zmath  isi
    3. A. Bensoussan, P. L Lions, “Optimal control of random evolutions”, Stochastics, 5:3 (1981), 169  crossref
    4. Pierre-Louis Lions, José-Luis Menaldi, “Optimal Control of Stochastic Integrals and Hamilton–Jacobi–Bellman Equations. II”, SIAM J Control Optim, 20:1 (1982), 82  crossref  mathscinet  zmath  isi
    5. P. L. Lions, “On the Hamilton–Jacobi–Bellman equations”, Acta Appl Math, 1:1 (1983), 17  crossref  mathscinet  zmath  isi
    6. P. L Linos, “Optimal control of diffustion processes and Hamilton–Jacobi–Bellman equations part I: the dynamic programming principle and application”, Communications in Partial Differential Equations, 8:10 (1983), 1101  crossref
    7. N. V. Krylov, “Smoothness of the value function for a controlled diffusion process in a domain”, Math. USSR-Izv., 34:1 (1990), 65–95  mathnet  crossref  mathscinet  zmath
    8. Zhou W., “A Probabilistic Approach to Interior Regularity of Fully Nonlinear Degenerate Elliptic Equations in Smooth Domains”, Appl. Math. Optim., 67:3 (2013), 419–452  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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