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@article{EMJ_2023_14_1_a4, author = {E. B. Laneev and E. Yu. Ponomarenko}, title = {On a linear inverse potential problem with approximate data on the potential field on an approximately given surface}, journal = {Eurasian mathematical journal}, pages = {55--70}, publisher = {mathdoc}, volume = {14}, number = {1}, year = {2023}, language = {en}, url = {http://geodesic.mathdoc.fr/item/EMJ_2023_14_1_a4/} }
TY - JOUR AU - E. B. Laneev AU - E. Yu. Ponomarenko TI - On a linear inverse potential problem with approximate data on the potential field on an approximately given surface JO - Eurasian mathematical journal PY - 2023 SP - 55 EP - 70 VL - 14 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/EMJ_2023_14_1_a4/ LA - en ID - EMJ_2023_14_1_a4 ER -
%0 Journal Article %A E. B. Laneev %A E. Yu. Ponomarenko %T On a linear inverse potential problem with approximate data on the potential field on an approximately given surface %J Eurasian mathematical journal %D 2023 %P 55-70 %V 14 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/EMJ_2023_14_1_a4/ %G en %F EMJ_2023_14_1_a4
E. B. Laneev; E. Yu. Ponomarenko. On a linear inverse potential problem with approximate data on the potential field on an approximately given surface. Eurasian mathematical journal, Tome 14 (2023) no. 1, pp. 55-70. http://geodesic.mathdoc.fr/item/EMJ_2023_14_1_a4/
[1] N. Y. Chernikova, E. B. Laneev, M. N. Muratov, E. Y. Ponomarenko, “On an inverse problem to a mixed problem for the Poisson equation”, Mathematical Analysis With Applications, CONCORD-90 2018, Springer Proceedings in Mathematics Statistics, 318, eds. Pinelas S., Kim A., Vlasov V., Springer, Cham, 2020, 141–146 | DOI | MR
[2] V. K. Ivanov, V. V. Vasin, V. P. Tanana, The theory of linear ill-posed problems and its applications, Nauka, M., 1978 (in Russian) | MR
[3] A. N. Kolmogorov, S. V. Fomin, Elements of function theory and functional analysis, Nauka, M., 1972 (in Russian) | MR
[4] E. B. Laneev, “On some statements of the continuation problem the potential field”, Bulletin of the RUDN. Physics Series, 8:1 (2000), 21–28 (in Russian)
[5] E. B. Laneev, “On the error of the periodic model of the problem of continuation of the potential field”, Bulletin of the RUDN. Physics Series, 9:1 (2001), 4–16 (in Russian)
[6] E. B. Laneev, “Construction of a Carleman function based on the Tikhonov regularization method in an ill-posed problem for the Laplace equation”, Differential Equations, 54:4 (2018), 476–485 | DOI | MR | Zbl
[7] E. B. Laneev, M. N. Muratov, “On the stable solution of a mixed boundary value problem for the Laplace equation with an approximately given boundary”, Bulletin of the RUDN. Mathematics Series, 9:1 (2002), 102–111 (in Russian) | Zbl
[8] A. I. Prilepko, “Inverse problems of potential theory”, Math. Notes, 14:5 (1973), 990–996 | DOI | MR
[9] L. N. Sretensky, “On the uniqueness of determining the shape of an attracting body by the values of its external potential”, Dokl. Akad. Nauk SSSR, 99:1 (1954), 21–22 (in Russian) | MR | Zbl
[10] A. N. Tikhonov, V. Ya. Arsenin, Methods for solving ill-posed problems, Nauka, M., 1986 (in Russian) | MR
[11] A. G. Yagola, Wang Yanfei, I. E. Stepanova, V. N. Titarenko, Inverse problems and methods of their solution, Applications to geophysics, BINOM. Knowledge Lab, M., 2014 (in Russian)