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Mat. Sb. (N.S.), 1986, Volume 130(172), Number 2(6), Pages 207–221 (Mi msb1865)  

This article is cited in 11 scientific papers (total in 11 papers)

On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale

N. V. Krylov


Abstract: Estimates are proved for the maximum of a solution of a linear parabolic equation in terms of the $\mathscr L_p$-norm of the right-hand side. The coefficients of the first derivatives are assumed to be integrable to a suitable power. Various boundary value problems are considered. Corresponding $\mathscr L_p$-estimates are proved also for the distributions of semimartingales.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 58:1, 207–221

Bibliographic databases:

UDC: 517.95
MSC: Primary 35K20, 60G48; Secondary 35B50, 60E99
Received: 10.06.1985

Citation: N. V. Krylov, “On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale”, Mat. Sb. (N.S.), 130(172):2(6) (1986), 207–221; Math. USSR-Sb., 58:1 (1987), 207–221

Citation in format AMSBIB
\Bibitem{Kry86}
\by N.~V.~Krylov
\paper On estimates of the maximum of a~solution of a~parabolic equation and estimates of the distribution of a~semimartingale
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 130(172)
\issue 2(6)
\pages 207--221
\mathnet{http://mi.mathnet.ru/msb1865}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=854972}
\zmath{https://zbmath.org/?q=an:0625.35041}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 1
\pages 207--221
\crossref{https://doi.org/10.1070/SM1987v058n01ABEH003100}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Khaled Bahlali, “Flows of homeomorphisms of stochastic differential equations with measurable drift”, Stochastics and Stochastic Reports, 67:1-2 (1999), 53  crossref  mathscinet  zmath
    2. Lieberman C.M., “The Maximum Principle for Equations with Composite Coefficients”, Electron. J. Differ. Equ., 2000, 38  mathscinet  zmath  isi
    3. Gyongy I., Martinez T., “On Stochastic Differential Equations with Locally Unbounded Drift”, Czech. Math. J., 51:4 (2001), 763–783  crossref  mathscinet  zmath  isi
    4. Zhang X., “Strong Solutions of SDEs with Singular Drift and Sobolev Diffusion Coefficients”, Stoch. Process. Their Appl., 115:11 (2005), 1805–1818  crossref  mathscinet  zmath  isi
    5. Sergei B. Kuksin, “On Distribution of Energy and Vorticity for Solutions of 2D Navier–Stokes Equation with Small Viscosity”, Comm Math Phys, 2008  crossref  mathscinet  isi
    6. Kurenok V.P., Lepeyev A.N., “On Multi-Dimensional SDEs with Locally Integrable Coefficients”, Rocky Mt. J. Math., 38:1 (2008), 139–174  crossref  mathscinet  zmath  isi
    7. Meyer-Brandis T., Proske F., “Construction of Strong Solutions of SDEs via Malliavin Calculus”, J. Funct. Anal., 258:11 (2010), 3922–3953  crossref  mathscinet  zmath  isi
    8. Zhang X., “Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients”, Electron. J. Probab., 16 (2011), 38, 1096–1116  crossref  mathscinet  zmath  isi
    9. Nazarov A.I., “A Centennial of the Zaremba-Hopf-Oleinik Lemma”, SIAM J. Math. Anal., 44:1 (2012), 437–453  crossref  mathscinet  zmath  isi  elib
    10. Krylov N.V., “An Ersatz Existence Theorem for Fully Nonlinear Parabolic Equations Without Convexity Assumptions”, SIAM J. Math. Anal., 45:6 (2013), 3331–3359  crossref  mathscinet  zmath  isi
    11. Chen G., “Non-divergence parabolic equations of second order with critical drift in Lebesgue spaces”, J. Differ. Equ., 262:3, 2 (2017), 2414–2448  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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