Geodesic
Approximation of smooth solutions to integral equations with degenerate kernels
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2156-2166 
A. A. Khromov. Approximation of smooth solutions to integral equations with degenerate kernels. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2156-2166. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A method is proposed for finding approximate smooth solutions to an integral equation of the second kind with a degenerate kernel. It is assumed that the inverse operator is unbounded.

[1] Mikhlin S. G., Lektsii po lineinym integralnym uravneniyam, Fizmatgiz, M., 1959 | MR

[2] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965 | MR

[3] Khromov A. A., Khromova G. V., “O nakhozhdenii priblizhenii k nepreryvnym resheniyam uravnenii I roda”, Zh. vychisl. matem. i matem. fiz., 49:2 (2009), 225–231 | MR | Zbl

[4] Khromov A. A., “O priblizhennom reshenii uravneniya pervogo roda s operatorom integrirovaniya”, Sovrem. metody teorii kraevykh zadach, Materialy Voronezhskoi vesennei matem. shkoly “Pontryaginskie chteniya-XIX”, Voronezhskii gos. un-t, Voronezh, 224–225

[5] Khromov A. A., “Priblizhenie reshenii prosteishego integralnogo uravneniya s pomoschyu summ Feiera”, Sovrem. probl. teorii funktsii i ikh prilozh., Tezisy dokl. XIV Saratovskoi zimnei shkoly, posv. pamyati akad. P. L. Ulyanova (28 yanv.–fevr. 2008 g.), Saratovskii gos. un-t, Saratov, 2008, 199–200