Geodesic
On overdetermined elliptic systems of pseudodifferential equations on a compact manifold
Sbornik. Mathematics, Tome 17 (1972) no. 4, pp. 539-550 
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/
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     title = {On overdetermined elliptic systems of pseudodifferential equations on a~compact manifold},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] M. S. Agranovich, “Ellipticheskie singulyarnye integro-differentsialnye operatory”, Uspekhi matem. nauk, XX:5(125) (1965), 3–120 | MR

[2] S. G. Mikhlin, Mnogomernye singulyarnye integraly i integralnye uravneniya, Fizmatgiz, Moskva, 1962 | Zbl

[3] M. I. Vishik, G. I. Eskin, “Uravneniya v svertkakh v ogranichennoi oblasti”, Uspekhi matem. nauk, XX:3(123) (1965), 90–152

[4] Dzh. Dzh. Kon, L. Nirenberg, Algebra psevdodifferentsialnykh operatorov, Psevdodifferentsialnye operatory, Mir, Moskva, 1967 | MR

[5] L. Khermander, Psevdodifferentsialnye operatory, Psevdodifferentsialnye operatory, Mir, Moskva, 1967 | MR

[6] B. R. Vainberg, V. V. Grushin, “Ravnomerno neellipticheskie sistemy. I”, Matem. sb., 72(114) (1964), 602–636 | MR

[7] A. Douglis, L. Nirenberg, “Interior estimates for elliptic cyctems of partial differential equations”, Comm. Pure Appl. Math., 8:4 (1955), 503–538 | DOI | MR | Zbl

[8] L. P. Volevich, “Ob obschikh sistemakh differentsialnykh uravnenii”, DAN SSSR, 132:1 (1960), 20–23 | Zbl

[9] L. Shvarts, Kompleksnye mnogoobraziya i ellipticheskie uravneniya, Mir, Moskva, 1964

[10] L. Khermander, Neellipticheskie kraevye zadachi, Psevdodifferentsialnye operatory, Mir, Moskva, 1967

[11] L. Khermander, “Otsenki v $L_2$ i teoremy suschestvovaniya dlya operatora $\overline\partial$”, Matematika, 10:2 (1966), 59–117

[12] E. S. Zukhovitskaya, “Kraevye zadachi dlya pereopredelennykh sistem differentsialnykh uravnenii”, DAN SSSR, 201:3 (1971), 523–526