Geodesic
On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 8, pp. 1363-1372 
A. P. Khromov; G. V. Khromova. On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 8, pp. 1363-1372. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_8_a0/
@article{ZVMMF_2012_52_8_a0,
     author = {A. P. Khromov and G. V. Khromova},
     title = {On the regularization of a~class of integral equations of the first kind whose kernels are discontinuous on the diagonals},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1363--1372},
     year = {2012},
     volume = {52},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_8_a0/}
}
TY  - JOUR
AU  - A. P. Khromov
AU  - G. V. Khromova
TI  - On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 1363
EP  - 1372
VL  - 52
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_8_a0/
LA  - ru
ID  - ZVMMF_2012_52_8_a0
ER  - 
%0 Journal Article
%A A. P. Khromov
%A G. V. Khromova
%T On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 1363-1372
%V 52
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_8_a0/
%G ru
%F ZVMMF_2012_52_8_a0

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

For a class of integral equations of the first kind whose kernels are discontinuous on the diagonals, the convergence of the Lavrent'ev regularization method is proved by using methods of the spectral theory of integral operators. These methods lead to a special Dirac system, and finding the asymptotics of fundamental solutions is an important part of the proof.

[1] Lavrentev M. M., O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki, Izd-vo SOAN SSSR, Novosibirsk, 1962 | MR

[2] Khromova G. V., “O skhodimosti metoda Lavrenteva”, Zh. vychisl. matem. i matem. fiz., 49:6 (2009), 958-965 | MR | Zbl

[3] Khromov A. P., “Integralnye operatory s yadrami, razryvnymi na lomanykh liniyakh”, Matem. sb., 197:11 (2006), 115-142 | DOI | MR | Zbl

[4] Khromov A. P., “Teoremy ravnoskhodimosti dlya integralnogo operatora s peremennym predelom integrirovaniya”, Metricheskaya teoriya funktsii i smezhnye voprosy analiza, Sb. statei, Izd-vo AFTs, M., 1999, 255–266 | MR

[5] Burlutskaya M. Sh., “Teorema ravnoskhodimosti dlya integralnogo operatora na prosteishem grafe s tsiklom”, Izv. Saratovskogo un-ta. Ser. Matem. Mekhan. Informatika, 8:4 (2008), 8–13

[6] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, Izd-vo inostr. lit., M., 1962