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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 1993 Volume 53, Issue 1, Pages 68–82 (Mi mzm3921)

This article is cited 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.

UDC: 517.944

Received: 12.11.1990


 English version:
Mathematical Notes, 1993, 53:1, 50–58

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