Geodesic
About the boundary value problem of Dirichlet type in the classes of quasiharmonic functions in a circle
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 5 (2011), pp. 62-67 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article the modified boundary value problem of the Dirichlet type in classes of quasiharmonic functions is considered. Solvability conditions and constructive algorithms for solving the classical Dirichlet boundary value problem in the classes of quasi-harmonic functions of the genus 2 are obtained. The boundary conditions are on the unit circle.
Keywords: boundary value problem, modified Dirichlet boundary value problem, quasi-harmonic functions, differential equations, unit circle. 
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     author = {K. M. Rasulov},
     title = {About the boundary value problem of {Dirichlet} type in the classes of quasiharmonic functions in a circle},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {62--67},
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K. M. Rasulov. About the boundary value problem of Dirichlet type in the classes of quasiharmonic functions in a circle. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 5 (2011), pp. 62-67. http://geodesic.mathdoc.fr/item/VYURM_2011_5_a8/

[1] Tihonov A. N., Samarskij A. A., The equations of mathematical physics, Nauka, M., 1972, 735 pp. (in Russ.)

[2] Tricomi F., Lectures on partial differential equations, M., 1957, 442 pp. (in Russ.)

[3] K. W. Bauer, “Uber eine der Differentialgleichung $(1+z\overline{z})^2W_{z\overline{z}}\pm n(n+1)W=0$ zugeordnete Funktionentheorie”, Bonner math., 23 (1965), 98

[4] R. Heersink, “Uber Lösungen der Bauer–Peschl–Gleichung und polyanalytische Funktionen”, Ber. Math.-Statist. Sek. Forschung. Joanneum, 268, 1986

[5] Rasulov K. M., “O reshenii kraevoj zadachi tipa Dirihle dlja uravnenija Baujera–Peshlja pervoj stepeni”, Sb. nauch. tr., Issledovanija po kraevym zadacham kompleksnogo analiza i differencial'nym uravnenijam, 8, Smolensk. gos. universitet, 2007, 62–70 (in Russ.)

[6] Privalov I. I., Boundary properties of analytic functions, M.–L., 1950, 337 pp. (in Russ.)

[7] Gahov F. D., Boundary value problems, Nauka, M., 1977, 640 pp. (in Russ.)

[8] Goluzin G. M., Geometric theory of functions of complex variable, Nauka, M., 1966, 630 pp. (in Russ.)

[9] Agoshkov V. I., Dubovskij P. B., Shutjaev V. P., Methods for solving problems of mathematical physics, Fizmatlit, M., 2002, 320 pp. (in Russ.)