Geodesic
An analytic formula for the index of an elliptic boundary-value problem
Sbornik. Mathematics, Tome 22 (1974) no. 1, pp. 61-90 
B. V. Fedosov. An analytic formula for the index of an elliptic boundary-value problem. Sbornik. Mathematics, Tome 22 (1974) no. 1, pp. 61-90. http://geodesic.mathdoc.fr/item/SM_1974_22_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An expression is obtained for an elliptic boundary-value problem $(A,B)$ in the form of a sum of two terms, one of which depends only on the properties of the operator $A$ at interior points of the domain, while the second depends on properties of $A$ and $B$ on the boundary. Each term is the difference of the traces of operators effectively constructed from $A$ and $B$. Bibliography: 11 titles.

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

[2] M. F. Atiyah, R. Bott, “The index problem for manifolds with boundary”, Bombay Colloq. on Diff. Analysis, Oxford Univ. Press., Oxford, 1964 | MR | Zbl

[3] L. Boutet de Monvel, “Boundary problems for pseudo-differential operators”, Acta Math., 126:1–2 (1971), 11–51 | MR | Zbl

[4] B. R. Vainberg, V. V. Grushin, “O ravnomerno neellipticheskikh zadachakh, II”, Matem. sb., 73 (115) (1967), 126–154 | MR | Zbl

[5] M. I. Vishik, G. I. Eskin, “Uravneniya v svertkakh v ogranichennoi oblasti”, Uspekhi matem. nauk, XX:3 (123) (1965), 89–152

[6] A. S. Dynin, “Ob indekse semeistv psevdodifferentsialnykh operatorov na mnogoobrazii s kraem”, DAN SSSR, 186:3 (1969), 506–508 | MR | Zbl

[7] R. T. Seeley, “The resolvent of an elliptic boundary problem”, Amer. J. Math., 91:4 (1969), 889–920 | DOI | MR | Zbl

[8] R. T. Seeley, “Analytic extensions of the trace, associated with boundary problem”, Amer. J. Math., 91:4 (1969), 963–983 | DOI | MR | Zbl

[9] B. V. Fedosov, “Ob indekse ellipticheskogo operatora v $R^n$ i ellipticheskoi granichnoi zadachi”, DAN SSSR, 207:3 (1972), 547–550 | MR | Zbl

[10] B. V. Fedosov, “Neposredstvennoe dokazatelstvo formuly dlya indeksa ellipticheskoi sistemy v evklidovom prostranstve”, Funkts. analiz, 4:4 (1970), 83–84 | MR | Zbl

[11] L. Khermander, Lineinye differentsialnye operatory v chastnykh proizvodnykh, izd-vo «Mir», Moskva, 1965