Geodesic
Positive solutions of linear quasielliptic evolution equations
Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 15-44 
V. A. Kondrat'ev; T. G. Pletneva; S. D. Èidel'man. Positive solutions of linear quasielliptic evolution equations. Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 15-44. http://geodesic.mathdoc.fr/item/SM_1972_18_1_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study a new class of elliptic equations whose characteristic surfaces are hyperplanes $t=\mathrm{const}$. We establish integrability of positive solutions of such equations with power weights in regions adjoining characteristic hyperplanes and in cylinders with generators parallel to the time axis. Information is obtained on the behavior of such solutions in unbounded regions. Examples which illustrate the accuracy of the results are mentioned. Bibliography: 7 titles.

[1] V. A. Kondratev, S. D. Eidelman, “O svoistvakh reshenii lineinykh evolyutsionnykh sistem s ellipticheskoi prostranstvennoi chastyu”, Matem. sb., 81(123) (1970), 398–429 | MR | Zbl

[2] T. G. Pletneva, S. D. Eidelman, “Teoremy o trekh tsilindrakh dlya reshenii lineinykh evolyutsionnykh kvaziellipticheskikh uravnenii”, DAN SSSR, 192:3 (1970), 507–510 | MR | Zbl

[3] T. G. Pletneva, S. D. Eidelman, V. A. Kondratev, “O polozhitelnykh resheniyakh ellipticheskikh uravnenii”, Matem. sb., 85(127) (1971), 586–609 | MR | Zbl

[4] A. S. Markus, S. D. Eidelman, “O matrichnykh zadachakh, voznikayuschikh pri izuchenii reshenii ellipticheskikh i parabolicheskikh uravnenii vtorogo poryadka”, Matem. issledovaniya, V, no. 2(16), Kishinev, 1970, 145–156 | MR

[5] L. Khermander, Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, Moskva, 1965 | MR

[6] S. D. Eidelman, Parabolicheskie sistemy, Nauka, Moskva, 1964 | MR | Zbl

[7] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, Moskva, 1967