Abstract:
Estimates are proved for the maximum of a solution of a linear parabolic equation in terms of the Lp-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 Lp-estimates are proved also for the distributions of semimartingales.
Bibliography: 16 titles.
Citation:
N. V. Krylov, “On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale”, Math. USSR-Sb., 58:1 (1987), 207–221
\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 Math. USSR-Sb.
\yr 1987
\vol 58
\issue 1
\pages 207--221
\mathnet{http://mi.mathnet.ru/eng/sm1865}
\crossref{https://doi.org/10.1070/SM1987v058n01ABEH003100}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=854972}
\zmath{https://zbmath.org/?q=an:0625.35041}
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https://www.mathnet.ru/eng/sm1865
https://doi.org/10.1070/SM1987v058n01ABEH003100
https://www.mathnet.ru/eng/sm/v172/i2/p207
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Xin Chen, Xue-Mei Li, “Strong completeness for a class of stochastic differential equations with irregular coefficients”, Electron. J. Probab., 19:none (2014)
Krylov N.V., “An Ersatz Existence Theorem for Fully Nonlinear Parabolic Equations Without Convexity Assumptions”, SIAM J. Math. Anal., 45:6 (2013), 3331–3359
Nazarov A.I., “A Centennial of the Zaremba-Hopf-Oleinik Lemma”, SIAM J. Math. Anal., 44:1 (2012), 437–453
Zhang X., “Stochastic Homeomorphism Flows of SDEs with Singular Drifts and Sobolev Diffusion Coefficients”, Electron. J. Probab., 16 (2011), 38, 1096–1116
Meyer-Brandis T., Proske F., “Construction of Strong Solutions of SDEs via Malliavin Calculus”, J. Funct. Anal., 258:11 (2010), 3922–3953
Sergei B. Kuksin, “On Distribution of Energy and Vorticity for Solutions of 2D Navier–Stokes Equation with Small Viscosity”, Comm Math Phys, 2008
Kurenok V.P., Lepeyev A.N., “On Multi-Dimensional SDEs with Locally Integrable Coefficients”, Rocky Mt. J. Math., 38:1 (2008), 139–174
Zhang X., “Strong Solutions of SDEs with Singular Drift and Sobolev Diffusion Coefficients”, Stoch. Process. Their Appl., 115:11 (2005), 1805–1818
Gyongy I., Martinez T., “On Stochastic Differential Equations with Locally Unbounded Drift”, Czech. Math. J., 51:4 (2001), 763–783
Lieberman C.M., “The Maximum Principle for Equations with Composite Coefficients”, Electron. J. Differ. Equ., 2000, 38
Khaled Bahlali, “Flows of homeomorphisms of stochastic differential equations with measurable drift”, Stochastics and Stochastic Reports, 67:1-2 (1999), 53
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