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Mat. Zametki, 1998, Volume 64, Issue 4, Pages 564–572 (Mi mz1431)  

This article is cited in 1 scientific paper (total in 1 paper)

A priori estimates of strong solutions of semilinear parabolic equations

G. G. Laptev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study an initial boundary value problem for the semilinear parabolic equation
$$ \frac{\partial u}{\partial t} +\sum_{|\alpha|\le2b}a_\alpha(x,t)D^\alpha u =f(x,t,u,Du,…,D^{2b-1}u), $$
where the left-hand side is a linear uniformly parabolic operator of order $2b$. We prove sufficient growth conditions on the function $f$ with respect to the variables $u,Du,…,D^{2b-1}u$, such that the apriori estimate of the norm of the solution in the Sobolev space $W_p^{2b,1}$ is expressible in terms of the low-order norm in the Lebesgue space of integrable functions $L_{l,m}$.

DOI: https://doi.org/10.4213/mzm1431

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English version:
Mathematical Notes, 1998, 64:4, 488–495

Bibliographic databases:

UDC: 517.956.4
Received: 25.06.1997

Citation: G. G. Laptev, “A priori estimates of strong solutions of semilinear parabolic equations”, Mat. Zametki, 64:4 (1998), 564–572; Math. Notes, 64:4 (1998), 488–495

Citation in format AMSBIB
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\by G.~G.~Laptev
\paper A priori estimates of strong solutions of semilinear parabolic equations
\jour Mat. Zametki
\yr 1998
\vol 64
\issue 4
\pages 564--572
\mathnet{http://mi.mathnet.ru/mz1431}
\crossref{https://doi.org/10.4213/mzm1431}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1687216}
\zmath{https://zbmath.org/?q=an:0920.35033}
\elib{http://elibrary.ru/item.asp?id=13276294}
\transl
\jour Math. Notes
\yr 1998
\vol 64
\issue 4
\pages 488--495
\crossref{https://doi.org/10.1007/BF02314630}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000079258700029}


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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. G. G. Laptev, “An Interpolation Method for Deriving a priori Estimates for Strong Solutions to Second-Order Semilinear Parabolic Equations”, Proc. Steklov Inst. Math., 227 (1999), 173–185  mathnet  mathscinet  zmath
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