Abstract:
We consider the overdetermined elliptic system of pseudodifferential equations
\begin{equation}
Pu=f
\end{equation}
on a smooth compact manifold $X$. We prove that for system (1) there exists a pseudodifferential compatibility operator $Q$ such that the condition $Qf=0$ is a necessary and sufficient condition for the normal solvability of the system in Sobolev–Slobodetskii spaces.
Bibliography: 12 titles.