RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1978, Volume 106(148), Number 2(6), Pages 214–233 (Mi msb2567)  

This article is cited in 5 scientific papers (total in 5 papers)

On passing to the limit in degenerate Bellman equations. I

N. V. Krylov


Abstract: In this paper the author proves theorems on passage to the limit in nonlinear parabolic equations of the form $Fu=0$, arising in the theory of optimal control of random processes of diffusion type. Under the assumptions that i) the functions $u_n$ and $u$ have bounded Sobolev derivatives in $t$, ii) the $u_n$ and $u$ are convex downwards in $x$, iii) the $u_n$ are uniformly bounded in some domain $Q$, iv) $u_n\to u$ a.e. in $Q$, v) the coefficients of linear combinations of $F$ satisfy certain smoothness conditions, it is proved that $Fu_n=0$ on $Q$ for all $n$ implies $Fu=0$ on $Q$. The second derivatives of the $u_n$ and $u$ with respect to $x$ are understood in the generalized sense (as measures), and the equations $Fu_n=0$ and $Fu=0$ are considered in the lattice of measures.
Bibliography: 10 titles.

Full text: PDF file (1874 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1978, 34:6, 765–783

Bibliographic databases:

UDC: 519.2+517.9
MSC: Primary 60J60; Secondary 93E20
Received: 27.04.1977

Citation: N. V. Krylov, “On passing to the limit in degenerate Bellman equations. I”, Mat. Sb. (N.S.), 106(148):2(6) (1978), 214–233; Math. USSR-Sb., 34:6 (1978), 765–783

Citation in format AMSBIB
\Bibitem{Kry78}
\by N.~V.~Krylov
\paper On passing to the limit in degenerate Bellman equations.~I
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 2(6)
\pages 214--233
\mathnet{http://mi.mathnet.ru/msb2567}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=503593}
\zmath{https://zbmath.org/?q=an:0403.35054|0445.35067}
\transl
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 6
\pages 765--783
\crossref{https://doi.org/10.1070/SM1978v034n06ABEH001356}


Linking options:
  • http://mi.mathnet.ru/eng/msb2567
  • http://mi.mathnet.ru/eng/msb/v148/i2/p214

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Cycle of papers

    This publication is cited in the following articles:
    1. N. V. Krylov, “On passing to the limit in degenerate Bellman equations. II”, Math. USSR-Sb., 35:3 (1979), 351–362  mathnet  crossref  mathscinet  zmath  isi
    2. N. V. Krylov, “Some new results in the theory of controlled diffusion processes”, Math. USSR-Sb., 37:1 (1980), 133–149  mathnet  crossref  mathscinet  zmath  isi
    3. N. V. Krylov, “On controlled diffusion processes with unbounded coefficients”, Math. USSR-Izv., 19:1 (1982), 41–64  mathnet  crossref  mathscinet  zmath
    4. Subbotin A. Subbotina N., “Optimum Result Function in the Problem of Control”, 266, no. 2, 1982, 294–299  mathscinet  zmath  isi
    5. P. L. Lions, “Optimal control of diffusion processes and Hamilton–Jacobi–Bellman equations part 2 : viscosity solutions and uniqueness”, Communications in Partial Differential Equations, 8:11 (1983), 1229  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:237
    Full text:61
    References:35

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019