Unique continuation of solutions of differential equations with weighted derivatives
Sbornik. Mathematics, Tome 191 (2000) no. 3, pp. 431-458 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper contains a generalization of Calderon's theorem on the local uniqueness of the solutions of the Cauchy problem for differential equations with weighted derivatives. Anisotropic estimates of Carleman type are obtained. A class of differential equations with weighted derivatives is distinguished in which germs of solutions have unique continuation with respect to part of the variables.
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     author = {N. A. Shananin},
     title = {Unique continuation of solutions of differential equations with weighted derivatives},
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     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_3_a7/}
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N. A. Shananin. Unique continuation of solutions of differential equations with weighted derivatives. Sbornik. Mathematics, Tome 191 (2000) no. 3, pp. 431-458. http://geodesic.mathdoc.fr/item/SM_2000_191_3_a7/

[1] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 1–4, Mir, M., 1987 | MR

[2] Plis A., “Linear elliptic differential equations without any solution in a sphere”, Comm. Pure Appl. Math., 14 (1961), 599–617 | DOI | MR | Zbl

[3] Calderon A. P., “Uniqueness in Cauchy problem for partial differential equations”, Amer. J. Math., 80 (1958), 16–36 | DOI | MR | Zbl

[4] Nirenberg L., “Lektsii o lineinykh differentsialnykh uravneniyakh s chastnymi proizvodnymi”, UMN, 30:4 (1975), 147–204 | MR | Zbl

[5] Trev F., Vvedenie v teoriyu psevdodifferentsialnykh operatorov i integralnykh operatorov Fure, T. 1, Mir, M., 1984 | Zbl

[6] Egorov Yu. V., Lineinye differentsialnye uravneniya glavnogo tipa, Nauka, M., 1984 | MR

[7] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1996 | MR

[8] Lascar R., “Propagation des singularités des solutions d'équations pseudo-différentielles quasi homogènes”, Ann. Inst. Fourier (Grenoble), 27 (1977), 79–123 | MR | Zbl

[9] Sakurai T., “Propagation of regularities of solutions to semilinear partial differential equations of quasi-homogeneous type”, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 33 (1986), 347–378 | MR | Zbl

[10] Kumano-go H., Pseudo-differential operators, MIT Press, London, 1984

[11] Eidelman S. D., Parabolicheskie sistemy, Nauka, M., 1964 | MR | Zbl

[12] Landis E. M., Oleinik O. A., “Obobschennaya analitichnost i nekotorye svyazannye s nei svoistva reshenii ellipticheskikh i parabolicheskikh uravnenii”, UMN, 29:2 (1974), 190–206 | MR | Zbl

[13] Kolmogorov A. N., Petrovskii I. G., Piskunov I. S., “Issledovanie uravneniya diffuzii, soedinennoi s vozrastaniem veschestva, i ego primeneniya k odnoi biologicheskoi probleme”, Byul. MGU. Matematika i mekhanika, 1:6 (1937), 1–26 | MR

[14] Zeldovich Ya. B., “K teorii rasprostraneniya plameni goreniya”, Zhurn. fiz. khimii, 22:1 (1948), 27–48 | MR

[15] Kadomtsev B. B., Petviashvili V. I., “Ob ustoichivosti uedinennykh voln v srede so slaboi dispersiei”, Dokl. AN SSSR, 192:4 (1970), 753–756 | Zbl