Geodesic
Mixed problem for a harmonic function
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 7, pp. 1094-1106 Cet article a éte moissonné depuis la source Math-Net.Ru

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A harmonic function is considered in a three-dimensional bounded domain. Its normal derivative is given on nearly the entire boundary of the domain, while the value of the harmonic function is specified on the remaining small portion. The method of matched asymptotic expansions is used to construct a complete uniform asymptotic expansion of the function in powers of a small parameter characterizing the size of the boundary portion with a specified function value. The asymptotic expansion is rigorously substantiated. 
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A. A. Ershov. Mixed problem for a harmonic function. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 7, pp. 1094-1106. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_7_a4/

[1] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, Izd-vo Inostr. lit., M., 1957

[2] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1976 | Zbl

[3] Ilin A. M., Uravneniya matematicheskoi fiziki, Nauka, M., 2009

[4] Polia G., Segë G., Izoperimetricheskie neravenstva v matematicheskoi fizike, Gosudarstvennoe izd-vo fiziko-matematicheskoi literatury, M., 1962

[5] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | Zbl

[6] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v 10 t., v. VIII, Elektrodinamika sploshnykh sred, Fizmatlit, M., 2005

[7] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989

[8] Ilin A. M., “Issledovanie asimptotiki resheniya ellipticheskoi kraevoi zadachi v oblasti s malym otverstiem”, Tr. seminara im. I. G. Petrovskogo, 6, 1982, 77–82

[9] Gadylshin R. R., “O vozmuschenii spektra Laplasiana pri smene tipa granichnogo usloviya na maloi chasti granitsy”, Zh. vychisl. matem. i matem. fiz., 36:7 (1996), 77–88

[10] Ershov A. A., “Asimptotika resheniya uravneniya Laplasa so smeshannymi usloviyami na granitse”, Zh. vychisl. matem. i matem. fiz., 51:6 (2011), 1064–1080 | Zbl

[11] Eskin G. I., Kraevye zadachi dlya ellipticheskikh psevdodifferentsialnykh uravnenii, Nauka, M., 1973

[12] Oleinik O. A., “Ob ustoichivosti zadachi Neimana”, Uspekhi matem. nauk, 11:1(67) (1956), 223–225