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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 6, Pages 1391–1413 (Mi izv2521)  

This article is cited in 7 scientific papers (total in 7 papers)

On the smoothness of solutions of degenerate elliptic equations

M. I. Freidlin


Abstract: It is shown that under broad assumptions the generalized solution of boundary problems for degenerate second-order equations satisfies a Hölder condition. An example is given which shows that increasing the smoothness of the data of the problem cannot alone achieve greater smoothness of the solution. Conditions are determined for existence of the derivatives of the generalized solution. The investigation is based on probability methods.

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:6, 1337–1359

Bibliographic databases:

UDC: 517.9
MSC: 35J70, 35B65, 35J25, 26B35, 35A05
Received: 13.09.1967

Citation: M. I. Freidlin, “On the smoothness of solutions of degenerate elliptic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 32:6 (1968), 1391–1413; Math. USSR-Izv., 2:6 (1968), 1337–1359

Citation in format AMSBIB
\Bibitem{Fre68}
\by M.~I.~Freidlin
\paper On the smoothness of solutions of degenerate elliptic equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 6
\pages 1391--1413
\mathnet{http://mi.mathnet.ru/izv2521}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=237944}
\zmath{https://zbmath.org/?q=an:0164.13301|0192.45102}
\transl
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 6
\pages 1337--1359
\crossref{https://doi.org/10.1070/IM1968v002n06ABEH000735}


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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. I. Freidlin, “O suschestvovanii v tselom gladkikh reshenii u vyrozhdayuschikhsya kvazilineinykh uravnenii”, UMN, 23:3(141) (1968), 187–188  mathnet  mathscinet  zmath
    2. M. I. Freidlin, “Existence “in the large” of smooth solutions of degenerate quasilinear equations”, Math. USSR-Sb., 7:3 (1969), 323–339  mathnet  crossref  mathscinet  zmath
    3. T. V. Maizenberg, “The Dirichlet problem for certain integro-differential equations”, Math. USSR-Izv., 3:3 (1969), 537–557  mathnet  crossref  mathscinet  zmath
    4. T. L. Maizenberg, “Ob odnom klasse integro-differentsialnykh uravnenii”, UMN, 24:1(145) (1969), 197–198  mathnet  mathscinet  zmath
    5. M. V. Safonov, “On the Dirichlet problem for Bellman's equation in a plane domain”, Math. USSR-Sb., 31:2 (1977), 231–248  mathnet  crossref  mathscinet  zmath  isi
    6. N. V. Krylov, “On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications”, Math. USSR-Sb., 64:2 (1989), 505–526  mathnet  crossref  mathscinet  zmath
    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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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