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Zapiski Nauchnykh Seminarov LOMI, 1986, Volume 152, Pages 21–44 (Mi znsl5115)  

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

Hölder estimates for weak solutions of generate parabolic equations

A. V. Ivanov
Full-text PDF (968 kB) Citations (1)
Abstract: We establish Hölder continuity, of solution of the degenerate parabolic equation
$$ \frac{\partial u}{\partial t}-\operatorname{div}\vec a(x,t,u,\nabla u)+b(x,t,u,\nabla u)=0, $$
where $\vec a$ and $b$ are required to satisfy following conditions:
\begin{gather*} |\vec a(x,t,u,\nabla u)|\leqslant\alpha_0|u|^{2\sigma}|p|+f_1(x,t),\\ \vec a(x,t,u,\nabla u)\cdot p\geqslant\nu_0|u|^{2\sigma}|p|^2+f_2^2(x,t),\\ |b(x,t,u,\nabla u)|\leqslant\beta_0|u|^{2\sigma}|p|^2+f_3^2(x,t), \end{gather*}
$\sigma\geqslant0$, $\nu_0>0$, $\alpha_0$, $\beta_0\geqslant0$, $f_i\in L_{q,q_0}(Q_T)$, $i=1,2,3$ with appropriate exponents $q$$q_0$. Interior estimates and estimates near the boundary of Holder exponents are obtained. Ho assumptions have been made concerning the sign of the solution.
Bibliographic databases:
Document Type: Article
UDC: 517.946
Language: Russian
Citation: A. V. Ivanov, “Hölder estimates for weak solutions of generate parabolic equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Zap. Nauchn. Sem. LOMI, 152, "Nauka", Leningrad. Otdel., Leningrad, 1986, 21–44
Citation in format AMSBIB
\Bibitem{Iva86}
\by A.~V.~Ivanov
\paper H\"older estimates for weak solutions of generate parabolic equations
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~18
\serial Zap. Nauchn. Sem. LOMI
\yr 1986
\vol 152
\pages 21--44
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl5115}
\zmath{https://zbmath.org/?q=an:0618.35066}
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  • https://www.mathnet.ru/eng/znsl/v152/p21
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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