Berezin, A. A theorem on the alternative for a degenerate problem with oblique derivative. (Russian. English summary) Zbl 0753.35036 Differ. Uravn. Primen. 45, 9-20 (1990). A second order degenerated elliptic system on a special domain \(\Omega_ m=\{x=(x',x_ n)\in\mathbb{R}^ n\), \(| x'|^ 2<1-| x_ n|^ m\}\), \(m\geq 2\), is considered with the boundary conditions \(\partial u/\partial x_ n=\phi\), on \(\partial\Omega_ m\), \(u=u_ 0\) on \(\partial\Omega_ m\cap\{x_ n=0\}\). An a priori estimate for the gradient of the solution is derived and an analogue of the Fredholm alternative is proved. Reviewer: A.Kufner (Praha) MSC: 35J70 Degenerate elliptic equations 35B45 A priori estimates in context of PDEs Keywords:oblique derivative; Fredholm alternative PDFBibTeX XMLCite \textit{A. Berezin}, Differ. Uravn. Primen. 45, 9--20 (1990; Zbl 0753.35036)