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Mathematics of the USSR-Sbornik, 1978, Volume 34, Issue 6, Pages 765–783
DOI: https://doi.org/10.1070/SM1978v034n06ABEH001356
(Mi sm2567)
 

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
References:
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.
Received: 27.04.1977
Bibliographic databases:
UDC: 519.2+517.9
MSC: Primary 60J60; Secondary 93E20
Language: English
Original paper language: Russian
Citation: N. V. Krylov, “On passing to the limit in degenerate Bellman equations. I”, 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 Math. USSR-Sb.
\yr 1978
\vol 34
\issue 6
\pages 765--783
\mathnet{http://mi.mathnet.ru//eng/sm2567}
\crossref{https://doi.org/10.1070/SM1978v034n06ABEH001356}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=503593}
\zmath{https://zbmath.org/?q=an:0403.35054|0445.35067}
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    Cycle of papers
    This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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