Geodesic
On local unsolvability and nonhypoellipticity of (pseudo-) differential equations with weighted symbols
Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 541-556 
N. A. Shananin. On local unsolvability and nonhypoellipticity of (pseudo-) differential equations with weighted symbols. Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 541-556. http://geodesic.mathdoc.fr/item/SM_1984_47_2_a15/
@article{SM_1984_47_2_a15,
     author = {N. A. Shananin},
     title = {On local unsolvability and nonhypoellipticity of (pseudo-) differential equations with weighted symbols},
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     volume = {47},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_47_2_a15/}
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This paper develops a procedure which enables one to construct microlocal asymptotic solutions of (pseudo-) differential equations with weighted symbols. Some theorems concerning local unsolvability and nonhypoellipticity are proved. Bibliography: 7 titles.

[1] Grushin V. V., Shananin N. A., “Nekotorye teoremy ob osobennostyakh differentsialnykh uravnenii so vzveshennymi simvolami”, Matem. sb., 103 (145) (1977), 37–51 | Zbl

[2] Khërmander L., “Psevdodifferentsialnye operatory i gipoellipticheskie uravneniya”, Psevdodifferentsialnye operatory, Mir, M., 1967, 297–367 | MR

[3] Kumano-go H., “Algebras of pseudo-differential operators”, J. Fac. Sci. Univ. Tokio Se I, 17 (1970), 31–50 | MR | Zbl

[4] Khërmander L., “Psevdodifferentsialnye operatory i neellipticheskie kraevye zadachi”, Psevdodifferentsialnye operatory, Mir, M., 1967, 166–296 | MR

[5] Shananin N. A., “O lokalnoi nerazreshimosti differentsialnykh uravnenii so vzveshennymi proizvodnymi”, Matem. sb., 111 (153) (1980), 465–477 | MR

[6] Nirenberg L., Treves F., “On local solvability of linear partial differential equations. Part I”, Comm. Pure Appl. Math., 23:1 (1970), 1–38 | DOI | MR | Zbl

[7] Khërmander L., Lineinye differentsialnye uravneniya s chastnymi proizvodnymi, Mir, M., 1965