Geodesic
On the Continuation of Solutions of Linear Equations with Analytic Coefficients
Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 921-928.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the tangent space, the principal symbol of the considered class of linear differential equations with analytic coefficients determines a bundle such that, on each of its integral lines, the germ of a generalized solution at one of the points uniquely determines the germs of the solution at all other points. The cases of holonomic and nonholonomic induces distributions are considered.
Mots-clés : unique continuation, solution germ. 
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N. A. Shananin. On the Continuation of Solutions of Linear Equations with Analytic Coefficients. Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 921-928. http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a10/

[1] J. M. Bony, “Une extension du théorème de Holmgren sur l'unicité du problème de Cauchi”, C. R. Acad. Sci. Paris Sér. A, 268 (1969), 1103–1106 | MR | Zbl

[2] L. Hörmander, “A remark on Holmgren's uniqueness theorem”, J. Differential Geometry, 6 (1971), 129–134 | MR | Zbl

[3] N. A. Shananin, “Ob odnoznachnom prodolzhenii reshenii differentsialnykh uravnenii so vzveshennymi proizvodnymi”, Matem. sb., 191:3 (2000), 113–142 | DOI | MR | Zbl

[4] N. A. Shananin, “Ob odnoznachnom prodolzhenii reshenii kvaziellipticheskikh uravnenii vtorogo poryadka”, Matem. zametki, 108:2 (2020), 316–320 | DOI | MR | Zbl

[5] K. Godbiion, Differentsialnaya geometriya i analiticheskaya mekhanika, Mir, M., 1973 | MR | Zbl

[6] L. Khermander, Analiz lineinykh differentsialrykh operatorov s chastnymi proizvodnymi. T. 3. Psevdodifferentsialnye operatory, Mir, M., 1987 | MR

[7] P. K. Rashevskii, “O soedinimosti lyubykh dvukh tochek vpolne negolonomnogo prostranstva dopustimoi liniei”, Uchen. zap. Mosk. gos. ped. in-ta im. K. Libnekhta. Ser. fiz.-matem., 3:2 (1938), 83–94

[8] W. L. Chow, “Über Systeme von linearen partiallen Differentialgleichungen erster Ordnung”, Math. Ann, 117 (1939), 98–105 | MR