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Mathematics of the USSR-Izvestiya, 1988, Volume 30, Issue 2, Pages 217–244
DOI: https://doi.org/10.1070/IM1988v030n02ABEH001002
(Mi im1292)
 

This article is cited in 4 scientific papers (total in 4 papers)

On the first boundary value problem for nonlinear degenerate elliptic equations

N. V. Krylov
References:
Abstract: This article is devoted to a proof of a general theorem on the existence of a solution of the first boundary value problem for a degenerate Bellman equation. In contrast to other papers the nonlinearity of the equation is used here and leads, for example, to a proof of solvability of the simplest Monge–Ampére equation $\det (u_{xx})=f^d(x)$ for $f \in C^2$, $f\geqslant0$ in a strictly convex region of class $C^3$ with zero data on the boundary.
Bibliography: 18 titles.
Received: 11.04.1985
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1987, Volume 51, Issue 2, Pages 242–269
Bibliographic databases:
UDC: 517.9
MSC: Primary 35A05, 35J25, 35J60, 35J70; Secondary 35J65
Language: English
Original paper language: Russian
Citation: N. V. Krylov, “On the first boundary value problem for nonlinear degenerate elliptic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987), 242–269; Math. USSR-Izv., 30:2 (1988), 217–244
Citation in format AMSBIB
\Bibitem{Kry87}
\by N.~V.~Krylov
\paper On~the first boundary value problem for nonlinear degenerate elliptic equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 2
\pages 242--269
\mathnet{http://mi.mathnet.ru/im1292}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=896996}
\zmath{https://zbmath.org/?q=an:0672.35025}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 2
\pages 217--244
\crossref{https://doi.org/10.1070/IM1988v030n02ABEH001002}
Linking options:
  • https://www.mathnet.ru/eng/im1292
  • https://doi.org/10.1070/IM1988v030n02ABEH001002
  • https://www.mathnet.ru/eng/im/v51/i2/p242
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:475
    Russian version PDF:128
    English version PDF:12
    References:49
    First page:1
     
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