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Zapiski Nauchnykh Seminarov LOMI, 1986, Volume 152, Pages 21–44
(Mi znsl5115)
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This article is cited in 1 scientific paper (total in 1 paper)
Hölder estimates for weak solutions of generate parabolic equations
A. V. Ivanov
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.
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
Linking options:
https://www.mathnet.ru/eng/znsl5115 https://www.mathnet.ru/eng/znsl/v152/p21
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