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This article is cited in 2 scientific papers (total in 2 papers)
Regularity of solutions of linear and quasilinear equations of elliptic type in divergence form
F. I. Mamedov Azerbaijan polytechnic Institute named after Ch. Il'drym
Abstract:
We prove estimates in $C(D)$ and $L_p(D)$ and in Orlicz norms of solutions of the following linear and quasilinear equations:
$$
\sum_{i,k=1}^n\frac\partial{\partial x_i}\biggl(a_{ik}(x)\frac{\partial u}{\partial x_k}\biggr)+\sum_{i=1}^n\frac\partial{\partial x_i}(b_i(x)u)+c(x)u=\sum_{i=1}^n\frac{\partial f^i}{\partial x_i}
$$
and
$$
\sum_{i=1}^n\frac\partial{\partial x_i}\bigl(a_i(x,u,\nabla u)\bigr)+h(x,u)=\sum_{i=1}^n\frac{\partial f^i}{\partial x_i},
$$
depending on the membership of the functions $c(x)$, $b_i(x)$ and $f^i(x)$ in various spaces $L_p(D)$. We write out explicitly the constants in the estimates obtained.
Received: 12.11.1990
Citation:
F. I. Mamedov, “Regularity of solutions of linear and quasilinear equations of elliptic type in divergence form”, Mat. Zametki, 53:1 (1993), 68–82; Math. Notes, 53:1 (1993), 50–58
Linking options:
https://www.mathnet.ru/eng/mzm3921 https://www.mathnet.ru/eng/mzm/v53/i1/p68
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Abstract page: | 262 | Full-text PDF : | 82 | First page: | 1 |
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