Fregman--Lindelof-type theorems for biharmonic functions

U. Yu. Zhuraeva

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2022), pp. 42-65.

Résumé

The work is devoted to the Fregman–Lindelof-type theorem for biharmonic functions, which is obtained using Carleman-type formulas.

Détail

Keywords: Fregman–Lindelof-type theorem, biharmonic function, Carlеman's function, integral representation.

Bibliographie

[1] Evgrafov M. A., Chegis I. A., “Obobschenie teoremy tipa Fragmena–Lindelefa dlya analiticheskikh funktsii na garmonicheskie funktsii v prostranstve”, DAN SSSP, 134:2 (1960), 259–262 | Zbl

[2] Chegis I. A., “Teorema tipa Fragmena–Lindelefa dlya garmonicheskikh funktsii v pryamougolnom tsilindre”, DAN SSSP, 136:3 (1961), 556–559 | MR | Zbl

[3] Arshon I. S., Evgrafov M. A., “O roste funktsii, garmonicheskikh v tsilindre i ogranichennykh na ego poverkhnosti vmeste s normalnoi proizvodnoi”, DAN SSSP, 142:4 (1962), 762–765 | MR | Zbl

[4] Arshon I. S., Evgrafov M. A., “Primer garmonicheskoi vo vsem prostranstve funktsii, ogranichennoi vne kruglogo tsilindra”, DAN SSSP, 143:1 (1962), 9–10 | MR | Zbl

[5] Arshon I. S., Evgrafov M. A., “O roste garmonicheskikh funktsii trekh peremennykh”, DAN SSSP, 147:4 (1962), 755–757 | MR | Zbl

[6] Leontev A. F., “O teoremakh tipa Fragmena–Lindelefa dlya garmonicheskikh funktsii v tsilindre”, Izv. AN SSSR. Ser. matem., 27:3 (1963), 661–676 | MR | Zbl

[7] Yarmukhamedov Sh. Ya., “Zadacha Koshi dlya poligarmonicheskogo uravneniya”, Dokl. RAN, 388:2 (2003), 162–165 | MR | Zbl

[8] Ashurova Z. R., Jurayeva N.Yu., Jurayeva U.Yu., “O nekotorykh svoistvakh yadro Yarmukhamedova”, International J. Inn. Research, 10:6 (2021), 84–90

[9] Ashurova Z. R., Jurayeva N.Yu., Jurayeva U.Yu., “Growing polyharmonic functions and the Cauchy problem”, J. Critical Rev., India, 7:7 (2020), 371–378

[10] Ashurova Z. R., Jurayeva N.Yu., Jurayeva U.Yu., “Task Cauchy and Carleman function”, Acad.: An International Multidisciplinary Research J., Affiliated to Kurukshetra Univ., Kurukshetra, India, 10:5 (2020), 1784–1789

[11] Goluzin G. M., “Obobschennaya formula Carleman'a i prilozhenie ee k analiticheckomu prodolzheniyu funktsii”, Matem. sb., 40:2 (1933), 144–149

[12] Tikhonov A. N., “Ob ustoichivosti obratnykh zadach”, DAN SSSR, 39:5 (1943), 195–198

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

[14] Yarmukhamedov Sh., “Formula Grina v beskonechnoi oblasti i ee primenenie”, DAN SSSR, 285:2 (1985), 305–308 | MR | Zbl

[15] Ashurova Z. R., “Teoremy tipa Fragmena–Lindelefa dlya garmonicheskikh funktsii mnogikh peremennykh”, DAN UzSSR, 1990, no. 5, 6–8 | MR | Zbl

[16] Zhuraeva N. Yu., Zhuraeva U.Yu, Saidov U. M., “Funktsiya Karlemana dlya poligarmonicheskikh funktsii dlya nekotorykh oblastei, lezhaschikh v $m$-mernom chetnom evklidovom prostranstve”, Uzbek Math. J., 2011, no. 3, 92–97 | MR

[17] Khasanov A. B., Tursunov F. R., “O zadache Koshi dlya uravneneiya Laplasa”, Ufimsk. matem. zhurn., 11:4 (2019), 92–106 | Zbl

[18] Khasanov A. B., Tursunov F. R., “Zadacha Koshi dlya trekhmernogo uravneniya Laplasa”, Izv. vuzov. Matem., 2021, no. 2, 56–73 | Zbl

[19] Vekua I. N., “Kompleksnoe predstavlenie reshenii ellipticheskikh differentsialnykh uravnenii i ego prilozhenii k granichnym zadacham”, Tr. Tbilisk. matem. in-ta, 1939, no. 7, 161–173