On the oblique derivative problem in the Sobolev space \(W^{s,p},\) \(p > 1\) (Q2577320)

This short communication deals with the oblique derivative problem for \(2r\), \(r\geq 1\), order linear elliptic partial differential equations. Depending on the structure of the boundary vector field near the set of tangency \(\Gamma_0\) two different cases are studied. In the first one an additional condition is imposed on the solution \(u\) on the manifold of tangency, namely \({\mathcal D}_n^ku|=u_{0k}\), \(k=0,1,\dots,\Gamma-1\). It is annouced in both cases that the boundary value problem under consideration is of Fredholm type and a priori estimates of the solutions \(u\) are shown in the scale of Sobolev spaces \(H^{s,p}(\Omega)\), \(p>1\). No proves are given.