Geodesic
Positive solutions of linear quasielliptic evolution equations
Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 15-44 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1972_18_1_a1,
     author = {V. A. Kondrat'ev and T. G. Pletneva and S. D. \`Eidel'man},
     title = {Positive solutions of linear quasielliptic evolution equations},
     journal = {Sbornik. Mathematics},
     pages = {15--44},
     year = {1972},
     volume = {18},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_1_a1/}
}
TY  - JOUR
AU  - V. A. Kondrat'ev
AU  - T. G. Pletneva
AU  - S. D. Èidel'man
TI  - Positive solutions of linear quasielliptic evolution equations
JO  - Sbornik. Mathematics
PY  - 1972
SP  - 15
EP  - 44
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1972_18_1_a1/
LA  - en
ID  - SM_1972_18_1_a1
ER  - 
%0 Journal Article
%A V. A. Kondrat'ev
%A T. G. Pletneva
%A S. D. Èidel'man
%T Positive solutions of linear quasielliptic evolution equations
%J Sbornik. Mathematics
%D 1972
%P 15-44
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1972_18_1_a1/
%G en
%F SM_1972_18_1_a1
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/

[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