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.
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
\Bibitem{Mam93}
\by F.~I.~Mamedov
\paper Regularity of solutions of linear and quasilinear equations of elliptic type in divergence form
\jour Mat. Zametki
\yr 1993
\vol 53
\issue 1
\pages 68--82
\mathnet{http://mi.mathnet.ru/mzm3921}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1215160}
\zmath{https://zbmath.org/?q=an:0838.35027}
\transl
\jour Math. Notes
\yr 1993
\vol 53
\issue 1
\pages 50--58
\crossref{https://doi.org/10.1007/BF01208522}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1993MY10400007}
Linking options:
https://www.mathnet.ru/eng/mzm3921
https://www.mathnet.ru/eng/mzm/v53/i1/p68
This publication is cited in the following 2 articles:
Maria Transirico, Sara Monsurrò, Farman Mamedov, Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015, 793
R. A. Amanov, F. I. Mamedov, “Regularity of the Solutions of Degenerate Elliptic Equations in Divergent Form”, Math. Notes, 83:1 (2008), 3–13