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Mat. Sb. (N.S.), 1983, Volume 121(163), Number 2(6), Pages 211–232 (Mi msb2187)  

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

On degenerate nonlinear elliptic equations. II

N. V. Krylov


Abstract: Dirichlet problems for degenerate nonlinear elliptic equations of Bellman type $\inf_p(L(p)u+f(p))=0$ are studied, where $L(p)$ is a linear elliptic operator of second order. Under certain conditions on the coefficients of $L(p)$, it is shown that this problem is solvable in the class of functions with bounded second derivatives.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1984, 49:1, 207–228

Bibliographic databases:

UDC: 517.9
MSC: Primary 35J70, 35J60; Secondary 35B45, 35A30
Received: 12.05.1982

Citation: N. V. Krylov, “On degenerate nonlinear elliptic equations. II”, Mat. Sb. (N.S.), 121(163):2(6) (1983), 211–232; Math. USSR-Sb., 49:1 (1984), 207–228

Citation in format AMSBIB
\Bibitem{Kry83}
\by N.~V.~Krylov
\paper On degenerate nonlinear elliptic equations.~II
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 121(163)
\issue 2(6)
\pages 211--232
\mathnet{http://mi.mathnet.ru/msb2187}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=703325}
\zmath{https://zbmath.org/?q=an:0549.35050|0538.35037}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 49
\issue 1
\pages 207--228
\crossref{https://doi.org/10.1070/SM1984v049n01ABEH002705}


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    This publication is cited in the following articles:
    1. L. Caffarelli, J. J. Kohn, L. Nirenberg, J. Spruck, “The Dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations”, Comm Pure Appl Math, 38:2 (1985), 209  crossref  mathscinet  zmath
    2. N. M. Ivochkina, “Solution of the Dirichlet problem for some equations of Monge–Aampére type”, Math. USSR-Sb., 56:2 (1987), 403–415  mathnet  crossref  mathscinet  zmath
    3. Kutev N., “On the Solvability of Monge-Ampere Type Equations”, 38, no. 10, 1985, 1283–1285  mathscinet  zmath  isi
    4. Bloss M., Hoppe R., “Numerical Computation of the Value Function of Optimally Controlled Stochastic Switching Processes by Multi-Grid Techniques”, Numer. Funct. Anal. Optim., 10:3-4 (1989), 275–304  crossref  mathscinet  isi
    5. Kutev N., Oliaro A., Popivanov P., “On the Solvability of the Characteristic Dirichlet Problem for Linear Degenerate Parabolic Equations”, Proc. Amer. Math. Soc., 138:1 (2010), 153–163  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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