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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 1, Pages 161–175 (Mi izv1638)  

This article is cited in 56 scientific papers (total in 57 papers)

A certain property of solutions of parabolic equations with measurable coefficients

N. V. Krylov, M. V. Safonov


Abstract: In this paper Harnack's inequality is proved and the Hölder exponent is estimated for solutions of parabolic equations in nondivergence form with measurable coefficients. No assumptions are imposed on the smallness of scatter of the eigenvalues of the coefficient matrix for the second derivatives.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:1, 151–164

Bibliographic databases:

UDC: 517.9
MSC: Primary 35K10, 35B99; Secondary 26D20
Received: 09.01.1979

Citation: N. V. Krylov, M. V. Safonov, “A certain property of solutions of parabolic equations with measurable coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980), 161–175; Math. USSR-Izv., 16:1 (1981), 151–164

Citation in format AMSBIB
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\paper A certain property of solutions of parabolic equations with measurable coefficients
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 1
\pages 161--175
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\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 1
\pages 151--164
\crossref{https://doi.org/10.1070/IM1981v016n01ABEH001283}
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    Citing articles on Google Scholar: Russian citations, English citations
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    1. V. V. Zhikov, M. M. Sirazhudinov, “The averaging of nondivergence second order elliptic and parabolic operators and the stabilization of solutions of the Cauchy problem”, Math. USSR-Sb., 44:2 (1983), 149–166  mathnet  crossref  mathscinet  zmath
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    5. A. A. Novruzov, “On an approach to the study of qualitative properties of solutions of nondivergence elliptic equations of second order”, Math. USSR-Sb., 50:2 (1985), 343–367  mathnet  crossref  mathscinet  zmath
    6. Paul E. Sacks, “Continuity of solutions of a singular parabolic equation”, Nonlinear Analysis: Theory, Methods & Applications, 7:4 (1983), 387  crossref
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