Geodesic
On Smoothness of a Solution to a Boundary Value Problem with Fractional Order Boundary Operator
Matematičeskie trudy, Tome 7 (2004) no. 1, pp. 189-199 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study a boundary value problem for the Laplace equation with a fractional derivative in the boundary condition. We prove the theorem of smoothness of a solution in the Nikol'skiĭ classes. 
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B. K. Turmetov. On Smoothness of a Solution to a Boundary Value Problem with Fractional Order Boundary Operator. Matematičeskie trudy, Tome 7 (2004) no. 1, pp. 189-199. http://geodesic.mathdoc.fr/item/MT_2004_7_1_a6/

[1] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961

[2] Bitsadze A. V., “K zadache Neimana dlya garmonicheskikh funktsii”, Dokl. AN SSSR, 311:1 (1990), 11–13 | Zbl

[3] Bugrov Ya. S., “Svoistva poligarmonicheskikh funktsii”, Izv. AN SSSR. Ser. mat., 22:4 (1958), 491–514 | MR

[4] Konyushkov A. A., “O klassakh Lipschitsa”, Izv. AN SSSR. Ser. mat., 21:3 (1957), 423–448 | MR | Zbl

[5] Natanson I. P., Konstruktivnaya teoriya funktsii, Gostekhizdat, M.; L., 1947

[6] Turmetov B. X., “Ob odnoi kraevoi zadachi dlya garmonicheskogo uravneniya”, Differents. uravneniya, 32:8 (1996), 1089–1092 | MR | Zbl

[7] Umarov S. R., “O nekotorykh kraevykh zadachakh dlya ellipticheskikh uravnenii s granichnym operatorom drobnogo poryadka”, Dokl. AN SSSR, 333:6 (1993), 708–710 | Zbl

[8] Gorenflo R., Luchko Y., Umarov S., “On the Cauchy and multipoint problems for partial pseudodifferential equations of fractional order”, Fract. Calc. Appl. Anal., 3:4 (2000), 249–275 | MR | Zbl

[9] Luchko Y., Gorenflo R., “The initial value problem for some fractional differential equations with the Caputo derivatives”, Acta Math. Vietnam., 24:2 (1999), 207–233 | MR | Zbl