Geodesic
Functions of several variables with bounded variation in ill-posed problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 36 (1996) no. 9, pp. 35-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. S. Leonov. Functions of several variables with bounded variation in ill-posed problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 36 (1996) no. 9, pp. 35-49. http://geodesic.mathdoc.fr/item/ZVMMF_1996_36_9_a4/

[1] Leonov A. S., “Kusochno-ravnomernaya regulyatsiya nekorrektnykh zadach s razryvnymi resheniyami”, Zh. vychisl. matem. i matem. fiz., 22:3 (1982), 516–531 | MR

[2] Leonov A. S., “O chislennoi realizatsii algoritmov kusochno-ravnomernoi regulyarizatsii”, Zh. vychisl. matem. i matem. fiz., 27:9 (1987), 1412–1416 | MR

[3] Tikhonov A. N., Goncharskii A. V., Stepanov V. V., Yagola A. G., Regulyariziruyuschie algoritmy i apriornaya informatsiya, Nauka, M., 1983 | MR

[4] Clarkson J. A., Adams C. R., “On definition of bounded variation for functions of two variables”, Trans. Amer. Math. Soc., 35:4 (1933), 824–854 | DOI | MR

[5] Vitushkin A. G., O mnogomernykh variatsiyakh, Gostekhteorizdat, M., 1955 | Zbl

[6] Shilov G. E., Gurevich B. L., Integral, mera, proizvodnaya, Nauka, M., 1967

[7] Ivanov L. D., Variatsii mnozhestv i funktsii, Nauka, M., 1975 | MR

[8] Giusti E., Minimal surfaces and functions of bounded variations, Birkhäuser, Boston etc., 1984 | MR | Zbl

[9] Adams C. R., Clarkson J. A., “Properties of functions $f(x, y)$ of bounded variation”, Trans. Amer. Math. Soc., 36:4 (1934), 711–730 | MR

[10] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974 | MR

[11] Hahn H., Theorie der reellen Funktionen, v. 1, Springer, Berlin, 1921

[12] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | MR | Zbl

[13] Young W. H., Young G. C., “On the discontinuities of monotone functions of several variables”, Proc. London Math. Soc. Ser. 2, 22 (1924), 124–142 | DOI

[14] Tikhonov A. H., Vasilev F. P., “Metody resheniya nekorrektnykh ekstremalnykh zadach”, Banach Center Publs., 3, 1975, 297–342 | MR

[15] Leonov A. C., “O nekotorykh algoritmakh resheniya nekorrektnykh ekstremalnykh zadach”, Matem. sb., 129(171):2 (1986), 218–231 | MR | Zbl

[16] Morozov V. A., Metody regulyarizatsii neustoichivykh zadach, Izd-vo MGU, M., 1987 | MR

[17] Leonov A. S., Chislennye algoritmy resheniya nelineinykh nekorrektnykh zadach s neapriornym vyborom parametra regulyarizatsii, Dep. v VINITI 15.01.88, No 346-V-88

[18] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978 | MR

[19] Pshenichnyi B. N., Danilin Yu. M., Chislennye metody v ekstremalnykh zadachakh, Nauka, M., 1975 | MR

[20] Tikhonov A. N., Goncharskii A. V., Stepanov V. V., Yagola A. G., Chislennye metody resheniya nekorrektnykh zadach, Nauka, M., 1990 | MR

[21] Bokhner S., Lektsii ob integralakh Fure, S dobavleniem avtora o monotonnykh funktsiyakh, integralakh Stiltesa i garmonicheskom analize, Fizmatgiz, M., 1962