Geodesic
On overdetermined elliptic systems of pseudodifferential equations on a~compact manifold
Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 539-550

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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. 
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     author = {E. S. Zukhovitskaya},
     title = {On overdetermined elliptic systems of pseudodifferential equations on a~compact manifold},
     journal = {Sbornik. Mathematics},
     pages = {539--550},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_17_4_a5/}
}
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E. S. Zukhovitskaya. On overdetermined elliptic systems of pseudodifferential equations on a~compact manifold. Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 539-550. http://geodesic.mathdoc.fr/item/SM_1972_17_4_a5/