Geodesic
Coefficient inverse problem for Poisson’s equation in a cylinder
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1849-1856 
V. V. Solov'ev. Coefficient inverse problem for Poisson’s equation in a cylinder. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1849-1856. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a8/
@article{ZVMMF_2011_51_10_a8,
     author = {V. V. Solov'ev},
     title = {Coefficient inverse problem for {Poisson{\textquoteright}s} equation in a~cylinder},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1849--1856},
     year = {2011},
     volume = {51},
     number = {10},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The inverse problem of determining the coefficient on the right-hand side of Poisson’s equation in a cylindrical domain is considered. The Dirichlet boundary value problem is studied. Two types of additional information (overdetermination) can be specified: (i) the trace of the solution to the boundary value problem on a manifold of lower dimension inside the domain and (ii) the normal derivative on a portion of the boundary. (Global) existence and uniqueness theorems are proved for the problems. The study is performed in the class of continuous functions whose derivatives satisfy a Hölder condition.

[1] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[2] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[3] Solovev V. V., “Obratnye zadachi opredeleniya istochnika i koeffitsienta v ellipticheskom uravnenii v pryamougolnike”, Zh. vychisl. matem. i matem. fiz., 47:8 (2007), 1365–1377 | MR

[4] Alifanov O. M., Identifikatsiya protsessov teploobmena letatelnykh apparatov (vvedenie v teoriyu obratnykh zadach), Nauka, M., 1979 | Zbl

[5] Anikanov Yu. E., Nekotorye metody issledovaniya mnogomernykh obratnykh zadach, Nauka, Novosibirsk, 1978

[6] Goldman N. L., Obratnye zadachi Stefana. Teoriya i metody resheniya, MGU, M., 1999

[7] Denisov A. M., Vvedenie v teoriyu obratnykh zadach, Nauka, M., 1994 | Zbl

[8] Lavrentev M. M., Romanov V. G., Shishatskii S. P., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980 | MR

[9] Romanov V. G., Obratnye zadachi matematicheskoi fiziki, Nauka, M., 1984 | MR

[10] Tikhonov A. N., Leonov A. S., Yagola A. G., Nelineinye nekorrektnye zadachi, Nauka, M., 1995 | MR

[11] Prilepko A. I., “Obratnye zadachi teorii potentsiala”, Matem. zametki, 14:11 (1973), 1560–1571

[12] Samarskii A. A., Vabischevich L. P., Chislennye metody resheniya obratnykh zadach matematicheskoi fiziki, Izd-vo “LKI”, M., 2007

[13] Belov Yu. Ya., Inverse problems for partial differential Equations, Utrecht etc., 2002 | MR

[14] Prilepko A. I., Orlovsky D. G., Vasin I. A., Methods for solving inverse problems in mathematical physics, Marcel Dekker Inc., New York–Basel, 2000 | MR | Zbl

[15] Isakov V., Inverse problems for partial differential equations, Springer, New York, etc., 1998 | MR | Zbl

[16] Leonov A. S., Reshenie nekorrektno postavlennykh zadach, URSS, M., 2009

[17] Krylov N. V., Nelineinye ellipticheskie i parabolicheskie uravneniya vtorogo poryadka, Nauka, M., 1985 | MR

[18] Safonov M. V., “Neravenstvo Kharnaka dlya ellipticheskikh uravnenii i gelderovost ikh reshenii”, Zap. nauchn. seminarov LOMI, 96, 1980, 272–287 | MR | Zbl

[19] Bogachev V. I., Smolyanov O. G., Deistvitelnyi i funktsionalnyi analiz: universitetskii kurs, NITs Regulyarnaya i khaotich. dinamika, M.–Izhevsk, 2009

[20] Khatson V., Pim Dzh., Prilozheniya funktsionalnogo analiza i teorii operatorov, Mir, M., 1983 | MR